Solution: until Apple sorts this out, I'm using an old USB optical mouse I had laying around. Gets the job done and tells me the issue is most likely with BlueTooth communication.

Same here. Magic Mouse 2 worked fine until I updated to Big Sur 11.2 this morning on my MBA 2017. I can click and scroll, but can't track with the Magic Mouse. The BT dropdown menu says it's connected, but in settings, showing 'no mouse detected'... Please fix!