FaceTime sound loop / echo on Mac

Over the past months, I had a few FaceTime calls with video (starting from Messages), and noticed that (especially when screen sharing is active) the sound is going into a resonance loop.

In the last call earlier today, I even had to "mute" the FaceTime audio to get rid of the resonance / echo. Strangely enough, the conversation could keep going, regardless of FaceTime being muted.

Even more strange is that after quitting FaceTime, the screen sharing (which was still open) kept going, including the sound I could hear from my conversation partner.

It seems to me that in these scenarios multiple channels are trying to transmit audio at the same time, causing closed loop resonance (potentially 3 channels : FaceTime, Messages, and Screensharing). How can I make sure that ONLY 1 CHANNEL is transmitting and receiving audio ?

Or is there a setting somewhere that I need to change to have the Mac automatically manage this (which is what I would expect from Apple as software designer in this case) ?

Looking forward to any feedback that could help with this issue ...