When I use a bluetooth audio device as both input and output, then quality is reduced.

"When I use a bluetooth audio device as both input and output, then quality is reduced.: [...]However, when I change the input to that bluetooth device as well, the audio output quality deteriorates. When I change the input back to MacBook Air Microphone, then the output quality goes back to normal."

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Troubleshooting Bluetooth Audio:

A. Reset the Bluetooth Module:

Reset the Bluetooth Module of the MacOS through use of Terminal. Thet would do its part in fixing some bugs in settings.

Use this Command:

sudo pkill bluetoothd

B. Try Safe Mode:

Boot Up in Safe Mode, and see if you no longer it.  Go here: Start up your Mac in safe mode - Apple Support, then, shut down the Mac, and power it back on, seeing if this has gone away. In Safe Mode, Login Items do not run at login, certain preferences are set aside, and damaged system files are then reset. 

C. Single-Out this User:

Create a new administrator user. Log into it, and see if you still get this message. If so, then it is an error with your current user. If not, then it is an error with you entire Mac.