Microphone activated when connecting bluetooth headphones / bad sound quality

I have the exact same problem as stated here: https://discussions.apple.com/thread/6879939

Since a few days, when I connect bluetooth headphones to my MacBook Pro (15 inch, 2016, macOS Mojave) I have very poor sound quality and I hear myself through the headphones (with using Oversight I also can see that the microphone gets activated).

Opening Audio MIDI Setup shows me that a poor output format is used (16k) - when I change it, it immediately switches back.

Force-quitting "coreaudiod" with the command line or Activity Monitor works - but then I cannot use the volume +- buttons on my mac (only on the headphones) to control the volume until I restart my Mac (which re-produces the behavior described above and I have to force-quit coreaudiod again).

Does anyone have a REAL, permanent solution for this problem?

It appeared out of nowhere and I have the problem with my Beats SOLO 3 as well as with Bose QC 35 II.

Thanks in advance.