I have an the Apple BT Mouse (yeah yeah, I know people hate it) and it’s paired to both my M1-Mini and my M1-MBP. I have ToothFairy installed on both macOS machines; each are running macOS 12.3.1.
When I tap the TF menubar icon to pause the connection on either (eg: M1-Mini), the mouse doesn’t pair on the M1-MBP. I’ve even tried using the native macOS BT menubar to force-connect the mouse. No go. Eventually, after about minute, the Apple mouse re-connects to the originating Mac, in this example the M1-Mini.