My teams also likes to go to "sleep" on my machine and just ignore incoming messages. I am embarrassed to get the email from exchange that I've missed a message in teams.
This is on a machine that is dedicated to teams and has nothing else running on it. It's got it's own monitor, is always in the foreground, and is something I can always see from my desk.
That, and my calendar no longer shows the time bar. So, I can see all my meetings, but I have to guess based on distance where in the day it's actually scheduled.
It's most definitely anti-productive to be using this.