I have the same issues on my mac (10.15.6)
Until two weeks ago my bluetooth headset (sony WX-1000XM3) works fine with Teams, but now they do not works any more.
Headset works with other applications until I try to make a call with teams or other applications (even a test call), then they stop works also with other applications.
So I suppose that the issue is related to the use of the headset microphone.
I've tried many time un unpair / pair headset, system reboot, SMC reset, etc.
All media permissions are on in teams settings.
Privacy settings for microphone on my mac are all on.
I got same results also with Apple Airpods.
UPDATE: September 2020.
Starting from the end of August all issues related to bluetooth headsets disappeared.
All my headsets (sony and apple) are working and I'm able to switch between headsets and my Mac microphone and speakers.
...but now, every time I start a Teams conference my Apple Magic Mouse stop working.
It disconnect from my Mac when the teams call begin, no way to connect it again during the Teams Call.
When the call is closed, after a few second the mouse reconnect.
I'm going crazy...