Damned if I can think of how changing the OS would affect an individual device being able to maintain communication with the Bluetooth controller.
kagis
https://www.reddit.com/r/bootcamp/comments/gcx5ug/solution_logitech_mx_master_mouse_dies_and_keeps/
This guy is talking about apparently at least a past model of that mouse having problems with Bluetooth power management and sporadic disconnections. The controller's power management configuration might depend on the OS. But that sounds like it happened after inactivity. You might try investigating that route.
Hmm.
I take it that this is a laptop? I guess one thing to try swapping out would be the Bluetooth controller. You can get little Bluetooth USB dongles on Amazon for like $4.
EDIT: Oh, just saw your other comment about needing USB ports.
