I have found a workaround, though it may be temporary as who knows what MS will do in July, using TEams Classic.
If you happen to have the Teams Classic app around, on a backup etc.
Ditch all remanents of New Teams, Teams 2, whatever you want to call it. If you boot Classic Teams with new Teams ANYWHERE on your system, it will find it and try to boot it. So put it in the trash and empty the trash.
Next, go to your User/Library folder and to the Containers folder - ditch anything mentioning Teams
Next, go to your User/Library folder and to Group Containers folder - ditch UBF8T folers that have .microsoft.teams at the end.
Empty your Trash.
Run Classic Teams from anywhere and it will boot. It's a little glitchy. After you log in the first time you'll see you're logged in but the window may be white and blank, with no info. Just quit Teams (don't just close the window) go back in and your info should populate ok.
Status blob sometimes takes a minute or so to switch to Green but I have it working, for now, on 5 Monterey Macs.
It will ask you if you want to continue using Teams Classic a few times, just say yes. You can even say 'Switch when I'm not using' as it cannot switch.
Not ideal but I hope this helps someone.