First loosing external mic, later external camera

[Prieni]

MacBook Air M2 on Sequoia 15.3 with connected monitor LG 27MD5KA (connected to the Mac via Thunderbolt 3 Dock), Zoom Workplace 6.2.11

I'm using Bluetooth headphones KEF Mu3 for meetings. As the microphone isn't too good usually I connect the headphones, select in the system settings the headphones for audio output, the microphone in the monitor for input before starting Zoom. 
Microphone and camera (also in the monitor) work fine. They are listed in the microphone and camera lists in Zoom, respectively.
Meeting starts and after a few minutes the mic vanishes (I cannot select it in the mic menu anymore). Choices left are MacBook mic (useless as the MacBook is closed), iPhone mic (tried that and lost it almost immediately with a message that the connection was lost) and the headphone mic (that turned out to work ok'ish).

A few minutes later the camera is lost as well. Choices are FaceTime HD camera (useless as the MacBook is closed) and iPhone camera (not really useful without a stand).

Funny thing is, when leaving Zoom the monitors microphone and camera remain disappeared (and only will come back after restart).

This doesn't happen in any other online meeting software (MS Teams, Webex, ...) and with Zoom it doesn't always happen. It has happened in December already, i.e. pre Sequoia and happened again today.

Any clues?