Managing sound and video settings during Teams meetings and calls for optimal communication
We're experiencing exactly what you have described. Resetting MS Teams cache appears to resolve the problem temporarily, but it does come back.
We experienced the feedback with headset to headset, headset to internal mic/speakers or webcam microphone and every combination of these.
Having said that, we could fairly reliably replicate the issue up until today's (18/03) update to New MS Teams. It's very early to say it's resolved, but so far it is looking better.
Windows 10 22H2 - New Teams Version - 24033.811.2738.2546
It would be nice to find any Teams update notes to see if and when things are changed.