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.
