Magic Mouse / Mice won't reconnect

I support my employer who moves his Mac Studio around to 3 locations. Each location has 2 Magic Mice, 2 Magic Keyboards with Keypad (some with touch ID), and a Belkin YourType keypad. These peripherals get unique names.

The issue is that the Magic Mice frequently won't connect when he moves to a different location, sometimes this will also happen after a restart in the same location. We have to keep wired mice on hand in order to delete and re-add the mice in Bluetooth Preferences.

We've experienced this problem across numerous Macs and operating systems for a decade now (Trashcan Mac Pro, iMac Pro, Mac Pro tower 2019, and now Mac Studio..... in most cases these machines were setup from scratch, Migration Assistant was not used). Along with typical resets I've trashed preferences and the like, nothing has worked.

Hoping someone may have some insight. Thank you!