I had mentioned this problem with my MacBook Air M1 and Magic Mouse Model A1657 here some time ago. Specifically, the trackpad functions of the mouse stop working, while moving the cursor and clicking are fine.
I have been dealing with the problem by hovering over the bluetooth icon at the top of the screen, turning the Magic Mouse OFF, then back ON, then enabling it with the mouse from the trackpad. This seems to work every time and doesn’t take very long.
However, I now have a new development to report. Several months ago, I had a problem with the screen turning pink and then crashing. I ran the M1 diagnostics and got the following result, "There may be an issue with the trackpad. Reference Code: NDR005, NDR006." Later, I read that the anti-virus software ClamXAV might be causing the Pink Screen crash, so I disabled it. No more crashes. Later I re-installed it and after awhile got another Pink Screen crash. So now it's gone.
However, I still have the trackpad diagnostic error. I was concerned about this, so I took the MacBook Air to the Genius Bar. They ran the diagnostic and found nothing. They kept it overnight and ran a complete series of tests with no problems (by the way the Magic Mouse was home on my desk - I did not even think there was a relationship).
Tonight I ran the diagnostic again and again got the trackpad error. For the first time thinking that there was a connection to the Magic Mouse problems, I turned the Mouse off and ran the diagnostic again with results that said, "No issues found. Reference Codes:ADP000."
I have repeated the diagnostic test several times. Magic Mouse on and connected gives trackpad errors. Magic Mouse off gives no errors.
Hopefully others are correct and Apple will fix this soon.