High level Clerics get the Divine Intervention feature, which has the following passage:

Describe the assistance you seek [...] The GM chooses the nature of the intervention; the effect of any cleric spell or cleric domain spell would be appropriate.

High level Arcana Clerics get the Arcane Mastery feature (SCAG, p. 126):

At 17th level, you choose four spells from the wizard spell list, one from each of the following levels: 6th, 7th, 8th and 9th. You add them to your list of domain spells. Like your other domain spells, they are always prepared and count as cleric spells for you.

...which lets them choose Wish as a cleric domain spell. The basic use of Wish is to replicate the effect of another spell, but some other Wish uses make the caster suffer Wish stress.

The stress of casting this spell to produce any effect other than duplicating another spell weakens you. After enduring that stress, each time you cast a spell until you finish a long rest, you take 1d10 necrotic damage per level of that spell. This damage can't be reduced or prevented in any way. In addition, your Strength drops to 3, if it isn't 3 or lower already, for 2d4 days. For each of those days that you spend resting and doing nothing more than light activity, your remaining recovery time decreases by 2 days. Finally, there is a 33 percent chance that you are unable to cast wish ever again if you suffer this stress.

What happens if an Arcana Cleric with Wish as its 9th level cleric domain spell makes a (successful) Divine Intervention and asks for a Stress-Inducing Wish (like granting a damage resistance to up to 10 creatures), assuming the GM rules that the god does indeed accept to grant the request as is (making a stressful Wish) ?

1. The Arcana Cleric is still the one who suffers the Wish stress (risking losing access to Wish)


2. The Cleric's god is the one who suffers the Wish stress (risking losing access to Wish)


3. No one suffers the Wish stress, since gods are too powerful to be affected by Wish stress


4. Other behaviour

All this assumes that the god is the one casting the spell during a Divine Intervention, which might not be accurate.

I'm asking this in the scope of Adventurers League play, although it might not matter.

Divine Intervention isn't spellcasting

An important distinction here is this...

Describe the assistance you seek [...] The GM chooses the nature of
the intervention; the effect of any cleric spell or cleric domain
spell would be appropriate.

The deity is not actually casting a spell. They are wielding their divine might to directly implement a miraculous outcome that may manifest as having the same output as a cleric or domain spell.

Thus, if your divine intervention request resulted in your Arcane Deity wielding the power of Wish on your behalf, they are skipping actually casting a spell, and just implementing the output directly. Since they are not casting Wish, they don't suffer any stress. They are just using their godly might to tinker with reality on your behalf.

However...

Divine Intervention isn't necessarily that precise.

Bear in mind that you do not have control over what your deity does or how powerfully they do it. Your prayer is for assistance. You are asking for aid...it's not a binding agreement where you get to tell your deity precisely what you want them to do. If you pray to your deity that you and your friends should be resistant to harm, they may just pop you all with Protection from Evil and Good, or an ongoing version of the Resistance Cantrip, or perhaps Stoneskin or even just Death Ward.

You cannot force a deity to cast a particular spell on your behalf, and they may not answer your plea for aid in quite the way you were expecting. Divine Intervention is a very powerful class feature, but it's not nearly as reliable as casting spells yourself.

Finally, the phrasing of that last line of the Feature Description is just a suggestion for how to implement Divine Intervention. It is a supplement to the first half. "The DM chooses the nature of the intervention" is the primary statement, supplemented by the suggestion to use the effect of a Cleric spell as the output. DMs are not confined to only using cleric spells.

If the DM deems it appropriate to go outside the bounds of cleric spells for a deity to grant a request for Divine Intervention, they can freely do so.

The divine intervention is not necessarily casting the spell

Deities are not limited to the same magic as mortals. While the Divine Intervention may replicate "the effect" of wish, the stress factor could not be involved.

lore note: Mystra of the Forgotten Realms limited mortal magic to 9th level spells¹, but deities are not limited in this way meaning they may have spells that have the power-level of wish without the risk

^{1: Lost Empires of Faerûn}

As you mentioned, the wording of Divine Intervention indicates that it would be appropriate to ask the deity to do this, but it doesn't specify how the deity grants the effect of a spell.

Thematically, you're praying to your deity, and they make your prayer become reality. You could technically argue that there is no casting of the Wish spell, your deity is just answering your prayers. I would also argue that a deity likely doesn't need to cast a spell to make something happen, they could just make reality bend how they choose, but that will come down to individual settings and how deities work for different DMs.

RAW, this seems to work. Wish here is indeed categorized as a cleric domain spell, and you wouldn't be casting the spell, so you wouldn't suffer the stress of the Wish.

However, it is my opinion that it is unlikely that this is intended to work. This seems like a bit of a loophole and it would fall to your DM to allow this to happen. Also note that Divine Intervention specifies:

The DM chooses the nature of the intervention...

So it would still fall to your DM to adjudicate this, regardless of whether or not this is RAW.

BUT...

This kind of effect is obviously limited to very high-level play, and epic happenings like this would certainly fit the gravitas of playing at level 17+. I think this is a neat idea, and I think I would allow something like this as long as the "Wish" isn't reality-breaking in some way.