Interesting. In my experience when on any Linux distribution I have to decide if I want good Audio quality and not use the microphone of the headset or if I want to use a worse audio code but activate the microphone. I thought this still was a widespread issue, or did I miss something?
My problem is not headphone specific but Bluetooth specific. It boils down to one of these questions, where there are multiple of to find. My deck also does not provite an answer and I can hear the audio quality difference massively between A2DP and other Codecs.
What kind of Daw are you using on Linux btw? I only know of Bitwig with Linux support. And I still did not get around to giving that a proper try.