This is a new issue. My headset worked fine with Teams as recently as yesterday.
Today I can start a Teams call, but when I tell my headset to connect to the call, the call drops. I have tried both connecting the paired headset to Teams after the call started, as well as pairing the headset to the computer after the call started. Each time the call simply drops. There is no error pop-up.
For anything else the headset works fine.
The wired headset works with Teams, as well.
I have (obviously) tried restarting the computer. It is a three year old homebrew using an AORUS mb running Windows 10 (64 bit) build 19045.3570, Windows Feature Experience Pack 1000.19052.1000.0
The version of Teams I'm currently using is 1.6.00.27573 (64 bit), which updated a week ago. The bluetooth drivers on the system haven't changed in ages.