This will be a quick post because I'm sure Logitech will fix this eventually (or maybe I'm the only person with this problem).
I have a Logitech M705 mouse I use extensively with my M1 Mac Mini. I configured one of the side buttons to launch Mission Control (to see all my windows instantly) - but this seems to crash some bit of Logitech code every once in a while (maybe once an hour this stops working for 1 minute, then starts working again).
Scroll to the bottom to see what fixed it for me.
While searching around for a fix, someone mentioned BetterTouchTool and it's ability to map actions to keyboard and mouse shortcuts - this was not my solution however. It got me thinking: what if instead of having the side button launch Mission Control, what if I set Logi Options to send a keyboard shortcut when pressing that side button?
Pressing Ctrl+Up launches Mission Control - so I configured the side button of my Logitech M705 to perform that keyboard shortcut using Logi Options. I uninstalled BetterTouchTool because I didn't need it for this fix. Now it works like a charm 100% of the time and never crashes!