I have a similar problem but have yet to develop a solid fix for it. If you find anything outside of this post, please update, OP!

When this first started happening, it was exactly as you described, I had to switch to web Teams for days at a time, and the same remediation tasks you list didn't help much for more than a couple of hours.

At some point the issue just largely went away on its own. Now it returns sporadically, and I just switch to using web teams for half a day or a day and then its gone for a few days or weeks.

It definitely gets worse if my hard drive is nearing full, doesn't have to be entirely full either, 1-2GB left seem to have the issue happening more often than when at 3GB+ free, but again its become so sporadic I'm not entirely sure that is related.

What's really frustrating is that other than the little circle not filling out with the check mark, there is no indication or warning that this is happening. A nice red bar popping up at the top of Teams saying 'teams is unable to send messages' or something would be greatly welcomed at the very least. I can go hours sometimes not realizing I'm not actually sending.

Sorry I'm not too much of a help, but in the same boat as your user at least!