Just an update on my version of Bluetooth issue which has ended happily albeit contingent on things working out consistanly over time.
Two developments have taken place which have lead to happy resolution.
i) Big Sur 11.2.1 came out and was installed.
ii) I had a chat with Apple this evening who were very helpful after they reached out in response to my comment on this thread.
The result of which is that I now understand that when you connect a bluetooth audio device in most cases the audio should be automatically routed through the device, however if you installed shims that install virtual audio input or output devices in the system one of these may be selected rather than your Blutooth device of choice. If you click the "control centre" icon in the menu bar and then click the word "Sound" above the silder it will show audio endpoints that audio can be routed to if there are more than one of these. Once I had selected the device I connected all seemed well for two devices. I am not sure if the OS will remember the choices between connections so I will have to monitor.
Moral of the story for me is that if it looks like your bluetooth audio device connects but your sound is stuck where it was click "Sound" in the "Control Centre" and check what sound endpoint is shown and make sure it is selected.
Hopefully this might help someone else in future.
It looks like 11.3 will likely drop in March so maybe further incremental improvements are made that fix the remainder of bluetooth issues as other updates have partially helped with.
Good luck to anyone else still struggling.