Do you have multiple MS Teams accounts? Either across multiple tenants or even just a single account connected to multiple organisations?
I have, and I’ve also been quite frustrated with the inability to stay signed in to each account and easily switch between them.
Turns out a lot of other people have been frustrated by this as well, as this is the number two item on UserVoice for MS Teams right now. So before you continue reading this workaround, head over and add your vote: