And the use case—a wallet that users are likely to sit on—is not the easiest in which to make a safe ultra-thin battery...

Normal airtags don't use rechargable lipos - they use a CR2032 coin cell battery

I know. I am entertaining the OP's exercise in how one might make a thinner device. CR2032s are more than 4 times as thick as a credit card, even without a socket or a housing.

The thinnest commonly available coin cells are 1.2mm thick, which is better, but still will require a creative interpretation of "credit card size".

An ISO credit card is 0.76mm thick.

How are you charging a LiPo in a CC sized device? How are you protecting it from the stresses of a wallet? Final problem with this - they'd give you 20-30Mah of power, which is nowhere near what you'd need for a decent battery life in one of these.

tldr; we're not there yet...

The easiest way to charge something thin would be a proprietary pogo-pin adapter and pads.

Protecting it would certainly be a challenge. If I were to try, my first attempt would be to sandwich it between two sheets of stainless. (0.76-0.4)/2 only leaves .18mm left over... that's 33 gauge. Maybe too thin to add enough rigidity? If you used 28 gauge stainless that would bring the sandwich to 1.04mm, which might be a better compromise.

It would certainly need some prototyping.

Apple gets 1 year of battery life from 225mah. So, it seems reasonable to get a month from 30mah. Not great, but hey, we're just entertaining the packaging requirement.