Curiously, it seems that (in my case, at least) there is some conflict with Chrome. I went into Sys Pref and Privacy to disable Chrome's access to the microphone and camera. Immediately, my bluetooth audio devices appear to work normally. I'm surprised and do not comprehend the possible relationship, but that is my experience today.... audio working all day long.

Circling back to confirm that the exact issue continues even with 12.3.1. update. Nothing has changed or been fixed. With some experimentation, the least-worst workaround for temporary improvement is: power down bluetooth device completely, disable Bluetooth on MacOS, play a video/audio file, then while it's playing re-enable Bluetooth in MacOS and power on the bluetooth device. Most of the time (not always) this results in normal audio quality in the headphones for a varying length of time (could be 5 minutes, could be 2 hours) before eventually it suddenly loses normal sound and/or disconnects entirely again. I hope that suggestion helps someone else manage to limp by until Apple finally learns how to make bluetooth work properly.