My answer: The only solution (besides the workaround with bluetooth explorer) I have found so far is switching to a bluetooth device which uses BT 4.0 or above.

And here some background findings:

- MS Sculpt Comfort Mouse and other BT 3.x devices are affected by this macOS bug

- MS Surface Mobile Mouse (BT 4.x) and probably other BT 4.x/5.x hardware is not affected
- the problem disappeared on my M1 Mac Mini during Big Sur 11.0 and 11.1, but as soon as Apple "fixed" its Bluetooth issues with 11.2, the problem reappeared.