I have many bad things to say about MS Teams, but it does allow you to join a meeting multiple times on multiple devices using the same user account - so you can watch a screenshare on your desktop. machine but use the microphone or camera on your phone.
Like you, I could speak for days about the problems with MS Teams, but this is definitely one of the things they get right. Handy for presenting your whole screen and being able to monitor chat conversations in that meeting on your iPad.
Funny that mentioned an iPad! I had the exact opposite use case: I used my iPad to draw a diagram, but used my desktop webcam instead of the one in the iPad sitting in my lap (which would have a terrible angle of pretty much only my chin).
I've noticed that it does this in meetings, but not in a direct chat with another person (I don't think group chats either). What I usually do in that case is create a meeting so that I can do that.