that might explain why ToothFairy works for me. and why previously Apple Music sometimes works half assed with Bluetooth -sometimes audio linked, sometimes no audio transmission but control of playback (on internal speakers).
I paid for installed the ToothFairy app in desperation. and after a shaky start, and a reboot (as a login item) I have found that it mostly enables connection to my bluetooth earbuds, but not my bluetooth mouse.
connection however still seems most reliable when audio is being continuously streamed.
note: it seems that it is best to ignore the label connected and disconnected and rely only on the evidence in your ears of connection, because the onscreen bluetooth connection status labels seem to be even more unreliable than the connection itself.
So it seems my initial conjecture that part of the issue is the power management of the bluetooth chip, may indeed be correct- despite Apples censor removing other posts regarding the issue because they were too speculative for the Apple Community discussion boards.