I'm cautiously optimistic to have fixed it, at least for now and the couple of devices I tried it on:
1. Uninstall Teams and reinstall from app store (probably not necessary, but doesn't hurt either).
2. You will be presented with the out of box experience, which has your previously used accounts conveniently listed. Do not tap any of them!
3. Instead, in the upper right of the screen, tap "Edit".
4. Remove all accounts from the list.
5. Re-add the MSA in Teams.