MacBook Pro (14-inch, 2021) M1 Pro 12.0.1 Same issue with my Logitech Mouse M275 mouse. Erratically stops working. Only a system reset temporarily fixes it. Super annoying.

Following the advice on this Reddit thread https://www.reddit.com/r/logitech/comments/qhk83k/mx_master_3_not_working_after_monterey_update_on/ I installed Logitech options+ and that fixed my problem. https://www.logitech.com/en-us/software/logi-options-plus.html#join-beta I granted the + app all the permissions that it asked for (2 of them) and did not have to reset my 2021 MBP 14'', scroll wheel started working immediately. I'm using a Logitech M275 mouse connected via a usb dongle.