Mac Mini 2018 Airpods no longer connect, rebooted, repaired multiple times, won't connect

So I'd hoped to fix this under Monterey, and upgrade to Ventura when I decided I was ready to do so, but trying to do a local rescue install of Monterey led to the dreaded preflight error 21 when trying to unlock my boot drive. So I went ahead and rescue Internet installed (option-cmd-R) Ventura, and so far the AirPods are working. I'll never know if merely Monterey needed to be reinstalled, which I wasn't able to test, or only upgrading to Ventura would have fixed it.

It's all very strange and I'd used the AirPods even under Monterey for many months without incident. I guess I'll never know why exactly this stopped working.

Nope.

Still broken. Today they won't connect, same behavior as before. So that's awesome. This is sadly so esoteric I know no one can help. Sad.

Came across a random thread that suggested trying as a new user, so I might try to see if it works as a new user on this system.

So trying a different user account doesn't work either. It paired fine, but then same issue.

They show up as discovered and pair in Console, there's interplay between bluetoothd and coreaudiod, but I can't make heads or tails of these messages, and never in my life have I found any useful resources for interpreting log messages anywhere on the entire Internet.

The saga continues. I worked through the pairing and resetting procedure over an hour and 30 minutes with several helpful support representatives; rebooting into safe mode briefly seemed to fix it, but once back in normal mode, they only connect for about 5-30 seconds, then disconnect. I have to put them back into the case and take them out for another 5-30 seconds, then disconnect again.

Not very useful.

I guess I need to call again and hope that I don't have to go through the original 1.5 hours again before proceeding to some new other approach or diagnostic.

I'd hoped safe mode really is magic, and somehow "fixes" things, but in this case that doesn't seem to be so; there's some root issue that must be resolved.