Are these many layers of misery inflicted upon innocents too much for a reader to handle?

You must be careful here: the way you phrase that statement, you appear to be laying the blame on the reader - "the story is good, but the reader is too weak for it". Consider instead the alternative approach: the reader is good, but you have not given him enough reason to care about your characters, substituted trauma for depth, and consequently bored the reader. This might not be the case, but this is a possibility you have to keep in mind.

Mark Twain famously criticised Fenimore Cooper's work:

[...] the author shall make the reader feel a deep interest in the personages of his tale and in their fate; and [...] he shall make the reader love the good people in the tale and hate the bad ones. But the reader of the "Deerslayer" tale dislikes the good people in it, is indifferent to the others, and wishes they would all get drowned together. (Mark Twain, Fenimore Cooper's Literary Offences)

How would your reader feel about your characters in the first chapter, when you start torturing them? Would he care, or would he "wish they would all get drowned together"?

Now, this might seem a strange notion: after all, shouldn't we care about a person being hurt by virtue of them being human? To some extent, we do. But we have only limited patience for the sob story of a person we don't know. When we're oversaturated, we close off, sympathy turns into boredom and rejection. It's like darkness-induced apathy, only applied to what happens with the characters, rather than the general setting.

It's not that we absolutely need sunshine and roses to connect to a character. What we need is the character having agency. You describe things done to the characters, more and more. They are victims, again and again. But we don't want to read about victims - we want to read about people struggling to stand in the face of adversity. Even if they fall in the end (e.g. 1984). There's an autobiographic book that came out recently: Born in the Ghetto: My Triumph Over Adversity by Ariella Abramovich-Sef. It doesn't start happy - it starts during the Holocaust, as you might have guessed from the title. But never does the author present herself as a victim. Again, from the title alone, this is a book about triumph, not about bad things happening to her.

M.R. Carey in The Girl with all the Gifts has an interesting way of avoiding inducing apathy with a dark start:

Now she's ten years old, and she has skin like a princess in a fairy tale; skin as white as snow. So she knows that when she grows up she'll be beautiful, with princes falling over themselves to climb her tower and rescue her.

Assuming, of course, that she has a tower.

In the meantime, she has the cell, the corridor, the classroom and the shower room.

[...]

After Sergeant says "Transit", Melanie gets dressed, quickly, in the white shift that hangs on the hook next to her door, a pair of white trousers from the receptacle in the wall, and the white pumps lined up under her bed. Then she sits down in the wheelchair at the foot of her bed, like she's been taught to do. She puts her hands on the arms of the chair and her feet on the footrests. [...]

Sergeant comes in with his gun and points it at her. Then two of Sergeant's people come in and tighten and buckle the straps of the chair around Melanie's wrists and ankles. There's also a strap for her neck; they tighten that one last of all, when her hands and feet are fastened up all the way, and they always do it from behind.

The setting is creepy, but the MC is very upbeat. The contrast creates curiosity. It's easy to sympathise with a girl who thinks of herself as a fairytale princess, and because we sympathise with her, we fear for her. Not the other way round.

When all else fails, there's gallows humour. All Quiet on the Western Front starts with this: "today we got double rations, because half the company got killed". Gallows humour too is a form of defiance, a form of agency. (And of course, Remarque doesn't rely on gallows humour alone - there's also strong camaraderie to build and maintain readers' sympathy.)

TL;DR: It's not about darkness alone. As others have pointed out, plenty of works from Dostoyevsky to Shakespeare are dark. Problem is, your readers must care about the characters, or you're inducing apathy. The character having some sort of agency goes a long way to help the reader connect with the character. If we want to read about suffering victims, there's always the news.

To a large extent this is will be dependent upon the taste of the person reading - so you have to work out who your target audience is and how you're trying to make them feel. There's nothing wrong with dark or "depressing" material but it won't to be everyone's tastes but what is?

What I would say is that you may want to insure that there is at least some lightness or reasons for optimism in the story as a whole. Not even The Bell Jar or The Lovely Bones are all depressing, all the time! This can be done either with moments of humor or hope for example.

...as are most of her companion's backstories

This leaped out a me a little bit, be careful not to overuse the tragic backstory trope - if everyone has a full on trauma conga line in their backstory then it will lessen the impact of each one. The same also applies to the more traumatic experiences you put the characters through during the story - throw too many at them at once and it lessens their impact. Consider spacing out some of your heavy hitting moments if you want to preserve maximum impact on the reader.

It's impossible to know if you've crossed the line because all we see is a summary. The summary sounds pretty brutal, but it's the execution that matters.

Yes, some books are hard to read. So much so that a lot of readers either won't try or will give up in the middle. The question for the reader is: is this book worth reading? That's true for any book but especially for one that is emotionally difficult.

If your novel engages your readers and brings something to them they can't get elsewhere, they will follow you through fire. If the story piles misery on misery for no good purpose, you will lose them.

Books that have done well with this issue include Dark Town, Mudbound, The Last Jew, and massive sections of Song of Ice and Fire (Game of Thrones and others).

No, I don't think from your summary that there's anything in your story that is 'too' depressing. I'll elaborate.

Are these many layers of misery inflicted upon innocents too much for a reader to handle?

Compared to some other books, the things you've described here don't really strike me as being particularly harsh.

Topics such as rape, torture, unfair treatment of a particular group of people are covered in airport novel thrillers all the time (not to mention movies), to the point that we're mostly desensitized to it.

Is there a fine line between dystopia and downright too much tragedy and sadness, and have I crossed it?

I think the fact that your novel is a dystopia means that people will find it easier to distance themselves from it, and not get too depressed, because at the end of the day it's just fiction.

Is there such a thing as a story being too dark?

In my opinion the kind of books that can really haunt you as a reader are much more likely to be ones based on true life, such as stories set in concentration camps, or based-on-a-true-story child abuse stories, or sex slave trafficking stories.

But even these stories, still have an audience. As is mentioned in the Wasp Factory, itself quite a challenging story in many ways, schadenfreude could easily support its own genre.

Whether they are 'too dark' is a matter of opinion. A friend of mine read The Leopard by Jo Nesbo and found the detailed torture so horrific that she (as a seasoned crime reader) not only refused to read any more of his books, but went and removedall of his children's books from her children's shelves. So for her, that was too dark. But that novel currently has 4.6 out of 5 on Amazon, so lots of people clearly find it a great read.

Similarly I know a lot of people who found some parts of Game of Thrones too upsetting to stick with, but others gobble it up.

When is misery justified?

In my opinion stories can be gratuitously violent and gruesome, and if they are, with no redeeming features, then I don't see much point in reading / watching them.

However, if stories cover difficult topics, and make us think about them in more depth - perhaps even opening our eyes to the suffering that is going on around us - then I think they have their place.

Are you overloading the misery in the intro?

On a slightly different note, and going a bit beyond the scope of your question, I am a bit concerned about the amount of suffering you want to put in the first chapter. Ensuring the characters are in a challenging situation and that the reader has sympathy for them is obviously a good thing, but if you lay it on too thick you risk alienating the reader as they might get fatigue from reading something so depressing without any sense of hope or enough identification with the characters.

Also, if you put too much in the beginning, that doesn't leave you with anywhere to go. It might be better to start with something really shocking. but then dial it right down so you can slowly build up the suffering again, once you've got the reader really on board and committed. This would be more effective at impacting their emotions as well.

TL;DR: The misery in your story sounds pretty tempered compared to other books / movies out there.

You're forgetting the power of contrast. What makes a grim or bleak story compelling is the moments of hope, the flashes of humor, the unexpected kindnesses, the oases of calm in the middle of the storms. If it's a tragedy, those are the moments that make the tragic parts heartrending. Absent those, you have only a colorless misery slog teetering on the brink of laughable self-parody.

You've certainly ramped up the grimdark a bit!

That said, I can think of a number of successful fantasy series which aren't a million miles away from yours. John Wyndham's The Crysalids is almost the scenario you describe, except that mutants are executed (although torture for information is a thing). The X-Men series is less horror-based but socially is very similar to your setup, including experimentation and vivisection. And The Handmaid's Tale book and TV series presents a fairly similar society if you consider "female" to be "the other".

On the grimdark front, you need to demonstrate a need for that grimdark to exist. If you can, then fine. But your character also needs to react appropriately to it, and not be miraculously unscathed. Sheri Tepper's Beauty is not a fluffy fantasy, but every step along the way is necessary. Stephen Donaldson's Thomas Covenant and Gap Cycle are probably even more intense than your setting. You might also consider the 2000s Battlestar Galactica reboot where humans take revenge for their losses by torturing captured Cylon hybrids, showing us Admiral Adama's moral core in comparison to Admiral Cain. And of course there's Game of Thrones.

So I don't think you need to be afraid of your setup being too depressing. What you need to do is have something to say about it. It may be hard to find something original to say which hasn't already been done by some of the examples above, but that's where your writing ability comes in. :)

Yes. Yes. And yes.

When I write, my rule of thumb is: if I start wondering whether something is too much, too off, or too something, it probably is.

The author is the mind and motor of the story, and they can tell the same story in a dark and gritty tone, as well as in a lighthearted and happy manner. If you have never tried, I'd recommend it as a great exercise. It is just like transposing a whole piece of music from major to minor. This being said, you reached a point where you find yourself wondering whether you have exaggerated in some dimensions of your story, perhaps in the dark tones, or in the comedic relief. The reason why you are wondering is that you have more or less consciously realized that exaggerating so much one dimension of reality without the rest of the frame to support it, has flattened your story to a one-dimensional sketch.

I wrote once half of a novel about a woman who embraces a sword to avenge her family. Two hundred pages later, when she was wading across a stream of blood, still wielding her weapon, fuming from the heat of the battle, I wondered whether that was too much. After all the story was about vengeance, and not an anatomy text-book on chopped meat.

In your example, I understand that you wish to convey the misery of your characters, and the hopelessness of their world. You could give a dry description of their background, as you mentioned in your summary. Or you could show the results of unnamed traumas. You could mention that not once have they been able to gather more than four hours of straight sleep without waking up amidst unspeakable nightmares. Or that they constantly look over their shoulders, as if someone should appear all of a sudden. Or that they don't like being touched. Or that the simple opening of doors can put them to shivers. Or that they are so light you can see the spine stick-out like a ridge between the shoulder-blades. Or that they are just made of bones so that when they fall, they sound like a handful of bamboo chopsticks bouncing and rolling on the floor. You can refer to the violence they received with broken words, and never fully describe it.

You ally in describing a grim and dark world is not your writing, but the imagination of your reader. Give them the right inputs, they will do the rest.

Now, I love dark things, but what I think is far more important than whether it's too dark is asking yourself why is it so dark. And the answer better isn't "cuz dis world be dark and dystopian". Does the guard have a motivation to rape that character beyond "he bad cause world dark" - maybe a personal hatred against her kind? What are you achieving from writing it like this? Do the incidents impact the story in a valuable way?

When I read through your description as is, my suspension of disbelief in that regard is broken. The darkness all just seems kind of there to me, when I think if you're gonna make it excessive, it should have a reason to be like that.

...This probably comes off harsher than I mean it. I'm not the story gospel and others might disagree with my "everything should have a why" point of view. It's still up to you in the end.

EDIT: I just thought about this a bit longer and came up with an example of what I mean. The atmokinetic could get raped specifically because she is so strong and the guard finds a fascination in overpowering somebody that powerful. The excessiveness of the torture in that case would be a testament to how meaningful it is to the guard to torture someone as big as her - and suddenly you have a rape scene that doubles as exposition :)

For a few points of comparison:

Our protagonist and her community live in a broken world ravaged by war. They are forced to work while enduring medieval conditions. Every year two dozen people are chosen by lottery to go and die (probably) in a blood-sport for the entertainment of the wealthy and powerful members of the terrifyingly powerful regime that controls the last vestiges of humanity.

The story kicks off when Protagonist's little sister, a rare flower of innocence in this awful place, is chosen for the blood sport and our Protagonist is forced to take her place.

The world of the Hunger Games is Horrible, Grimdark and Obscene. It's also a really good setting for the story. The story is about Katniss's mission to survive and later to overthrow the corrupt regime, it's fundamentally an underdog story. Struggle and Trials drive the plot against a background of oppression.

For contrast, an animated series full of anthropomorphic brightly coloured animals can feature a bleak manic-depressed protagonist and be such a crushing downer that I can't keep watching it for long.
Bojack Horseman is a hard watch for me, but it's so compelling that I keep coming back to it. It makes me feel things, not always good things, but it's a journey.

Then there's the world of Warhammer 40k. Practically the Trope-Namer for Grimdark. A sci-fi setting where Hell is a real place, Daemons want your soul, alien monsters want to eat you and the good guys are an Evil Theocratic Empire in a millenia-slow death spiral.

As the opening text for every book in that universe goes "There is no peace amongst the stars, only an eternity of carnage and slaughter, and the laughter of thirsting gods."

Warhammer gets away with it because it's so insanely over the top that it's impossible to take seriously.

How you write it is everything, a well crafted story can be grimdark without being depressing, though sometimes the depression can be the point too.

Black Mirror as a franchise basically is intended to evoke grimdark and depression in its audience. It's popular because like any other media, the point is to present emotion and experiences for the audience to experience that they might not otherwise. Some people find depressing material compelling. I'm not one of them, but that's okay.

I think with your bleak setting, you need to decide how you want to tell your story, what kind of story is it? Are your protagonists attempting to change the status quo? Will they succeed?
If they're just going to be crushed and stepped on endlessly for 300 pages then it's probably not a story I would want to read.

I had enough of that with Orwell's 1984.

Honestly though, write your story. Don't worry about your audience, if you're happy with the result then rest assured there will be many many other people who will be too.

You need Karmic Justice. Great Pains = Great Rewards.

Readers expect suffering of heroes to be rewarded by success, and suffering of victims to be revenged. If good guys die in war, they want the war to be won by the good guys, so their deaths meant something, or made a difference.

This is part of the psychology of reading fiction. Most of us, IRL, have suffered hardships for no reason, been abused by bullies, mean teachers, mean bosses, and gotten nothing for it. We know (directly or indirectly) good people that have suffered and died of disease for no apparent reason; rich jerks that deserve to die but don't, victims of crime, rape and murder, with no perpetrator ever brought to justice.

Karmic Justice is the Buddhist idea that the evil one puts into the world will be returned to them in kind; in this life or the next. Most people want it to be in this life, of course!

So if your heroes suffer horribly and there is a lot of one-sided suffering, then the payoff of their determination and whatever system or villain they vanquish should be proportionate to the pain they suffered. To the reader, it has to feel like the pain was necessary to accomplish the goal.

Even the people that died. Some may die to prove how deadly the enemy is (or how deadly the hero is). Otherwise, when people suffer and die, it should motivate the heroes in some way, to act, to take risks, to get revenge. That is the value of creating sacrificial companions and friends.

Without Karmic Justice you don't have a satisfying ending. Evil already prevails IRL, we want our fiction to escape the injustices of real life, show us heroes that suffer but (unlike real life) find a way to prevail. That's the fun of the fantasy. To be special. To be powerful. To overcome being a victim, and have the courage to risk it all and defeat the greatest evil.

So that is what you need to weave into these tales of suffering. Anger at other people's pain, determination to defy the system, despite the personal pain it will cause. You show the suffering in order to show the decisions it is forcing for the heroes. A story needs causality, the suffering should cause something to change in the hero, that should cause more things and eventually the suffering is "paid off" by the good the hero has brought to the world, not just for herself. We want the Pain to be dwarfed by the Good.

No, you world is not too dark

Before I continue, let me clarify that statement: your world is not too dark for most people, and equally dark (or darker) settings have seen wild success.

Settings of that tone have succeeded across a variety of media. Though I can only speculate as to why, I can certainly give some examples.

Have you heard of The Walking Dead? The premise is that zombies are real and have caused a global collapse of society. One of the central tenets of this series is that, even with real monsters out and about, the thing that humans must fear the most are each other. The plot is full of examples of humans betraying one another, people giving in to their darkest impulses, well-intentioned people's mistakes getting beloved characters killed abruptly and unceremoniously, and carries an over feeling of bleak fatalism. It doesn't take very long at all to make the reader/viewer wonder whether the title is referring to the hordes of zombies outside, or the few survivors struggling to make it to tomorrow.

Then there's Game of Thrones. If you haven't heard of that, you might have been living under a rock. One of the most common refrains throughout the books is a phrase that translates to "All men must die," and this is a theme that follows the entire series. The reader becomes afraid to get attached to any character because so many likeable characters are abruptly, sometimes arbitrarily, killed. Any clash between opposing sides becomes a frightening ordeal for the reader, because no matter who wins, the reader knows that somebody they like will end up dead. "Main Character" status is almost irrelevant, because, as George R. R. Martin once answered when asked why he killed so many MCs, "I can always just make another." Yet, this series has been wildly successful, sparking a mainstream HBO series by the same name!

In yet another form of media, there is the Grimdark setting of Warhammer: 40k. This is a dystopian sci-fi setting where everything is bad, the good guys are still the bad guys, and daemons are going to eat all of our souls, unless the space bugs from other galaxies eat us first, assuming that the space robot magic zombies don't wipe out all life before that, assuming we don't accidently destroy ourselves first by creating another evil god and all getting eaten by it. Essentially, everything is bad all the time, and it almost always only goes from bad to worse.

Even so, the setting has sparked a rather ridiculous number of books written in that setting, and has one of the most popular tabletop wargames tied intrinsically to this setting.

The thing about all of these is that their darkness is, for the most part, written or handled well. But, all of them are dark. Each of them has scenes and plot threads every bit as brutal and bitter as the one you have described, but people keep reading them.

So no, your setting is not too dark to succeed.

While I believe that you can't completely determine whether a story is too dark from the summary alone, I also have gotten a strong sense of what I think is most likely to be the case.

I think your story is not too dark, but it may be too graphic. Based on the outline you provided, you are throwing the readers into a world of cruelty and torture from the very beginning. Unfortunately, at this point, the reader has not yet developed a bond with the characters and all this torture will not provoke their sympathetic emotions in the way you might expect. The reader hasn't had enough time to truly care about the characters yet. "Darkness" ties in strongly with emotion and the readers' reaction. You want your readers to connect with the character and feel, "Oh God, that's horrible! She doesn't deserve this." when they read the tragic parts, instead of "This is inhumane, but lots of people suffer this in real life. I don't really care about this character in particular." There is not enough emotional depth for it to be considered dark yet.

Since I have to give a reference apparently, think about popular dystopian novels like Divergent or the Hunger Games. Both books start at a relatively peaceful, non-traumatic point in the main character's life, so the reader can get a feel for who they are and relate to them as they go through daily life and may have some relatable thoughts. Later, the horror of what happens provides a significant contrast and allows the reader to question the cruelty of the dystopian society, because they have a reference point.

On the other hand, if you do nothing but subject the characters to torture, torture, and torture, it may escalate to the point where readers are turned off because it's getting too graphic. Don't hurt your characters excessively for the sake of hurting them. The reader will probably see right through that. So, while your story so far is not too dark, do your best to not make it too graphic.

It depends on what your goals are. For mass consumption, you might want to tone it down. If you are happy with a smaller customer base, then you probably will find a reader for just about any atrocity.

For myself, I have no trouble reading rather graphical details, if everything else is interesting in its own way (i.e., not only because of the gore), and if the brutality is plausible in-universe.

For example: The works of Neal Asher are always working great for me. He has a knack for mutilating and outright torturing characters; not in a prison cell at the hands of a torturer, but in various interesting ways. One of his memes is characters changing themselves (psychologically and physically) voluntarily in quite advanced, disruptive, hard-Sci-Fi ways, spanning large parts of the story line, with regular ups and downs. While he does use occasional graphical descriptions, it never seems to be just "for fun", but mostly is very well founded and inevitable in the internal logic of his universe.

One of the most memorable descriptions of his were those that were specifically not in-detail, but, for example, only detailled the end result or a specific short highlight during the troubles a character went through.

Another example which absolutely did not work for me was the "Wizard's First Rule", where, quoting Wikipedia,

[the hero] falls into the hands of a Mord-Sith named Denna who brutally tortures him for a month

I remember that I liked the book at the beginning, but was quickly being put off by the quite long-winded graphical and emotional torture. It's not that I was particularly squeamish about it (it's so "far out" that it's almost unrealistic, especially considering the victim does not have magic during these sessions, so is basically a relatively normal human), but I felt it was just boring and pointless, almost like fan service.