Lack of updates isn’t a killer as much as you think. I’m intentionally running a 5 year old version of Android (11) and never once have any security issues. The best defense is being smart about your usage no matter how old your software is.

Honestly just get a new mouse and consider this a lesson to be a bit more careful next time. The amount of effort to fix your current mouse isn’t worth your time

Put it towards rent, shit’s insane these days

Fingerprinting. If they don’t have a cookie, they’ll link other information that they have to figure out with pretty decent accuracy who you are