How common is the passive (bí déanta ag...) in Irish? The autonomous seems to be a lot more common; I guess it would have to be used to express agency (Déantar ag... doesn’t seem to make sense), but are there other situations where it’s often used?

There are
591 hits for "déantar"
1342 hits for "déanta ag ..." of which:
194 hits for "déanta agam"
128 hits for "déanta agat"
343 hits for "déanta aige"
122 hits for "déanta aici"
77 hits for "déanta againn"
16 hits for "déanta agaibh"
139 hits for "déanta acu"
in The New Corpus for Ireland (native speakers only)

Déanta ag is primarily a perfect tense, more precisely a resultative aspect, i.e. the result (not the action) has prority.
It is formally a passive but it isn't felt passive voice, because tá ... agam means I have.
e.g.
Anois féach cad atá déanta agaibh! (Now look what you have done! i.e. Look at the result of your doing!)
Tá obair dhá lá déanta agaibh ( You have done the work of two days ... and here we all can see the result)

Déantar is active and action orientated. It isn't passive at all (only the English translation is).
And you can't express agency (not: déantar agam é, only déantar é = one does it / it is done)

Alright, can déanta ag function as the intended passive if necessary (e.g. Bhí sé déanta ag céadta daoine), or is it something else?

When the focus is on the actor or action, active voice is usually better:
Rinne na céadta duine/daoine é.

(céadta usually with article)

So there really isn’t much of a passive in Irish at all?

Go díreach.

Alright, thanks, but to be clear, the past participle + ag can be used as the intended passive if you really want it to be?

Yes, within its limitations.
Generally, passive voice is less used in Irish and active forms are usually always preferred*). You need to have a "good reason" for passive, a much better reason than in English.
The same is true for perfect tenses. And "tá déanta agam" is both: passive and perfect.

* an exception:
In case of progressive forms, Munster dialect prefers passive forms when the object of the action is antecedent of a relative clause;
e.g.: an rud atá mé a dhéanamh (Standard)-> an rud atá á dhéanamh agam (Munster). = the thing that I'm doing -> the thing which is being done by me

Alright, once again, thanks a lot. Sometimes people like you are the best resource available online, the state of online grammar resources for Irish is...not good at the moment.