This is a long story and I hope you bear with me. About a month ago I started having this issue. As soon as I opened up AI the mouse would just freeze as soon as I clicked into a document. The mouse worked everywhere else. this happened with the magic mouse, wired mouse, and tablet.
After contacting Adobe help and letting a tech assist get access to my computer, they were able to do something to make it work. This issue would only happen on my end, not their's. Every time it would take about 45 minutes to resolve the issue, but unfortunately, it would happen again a couple of days later.
I've contact Adobe at least 7 times in the last month to resolve this (it's the program I use for all freelance work). Within the last month, I reinstalled the current version of AI multiple times, installed older versions of Illustrator, had my Mac inspected by Apple, quadrupled my RAM, unplugged any external drives, started in safe mode, removed any problematic files and it still kept on happening. My iMac is all up-to-date and running on the most current version of MacOS Monterey. Because the Adobe techs attempted to solve this issue in so many ways it was hard to keep up with what was done that solved the issue.
The last time an Adobe tech helped, they went into the AI Preferences then User Interface, and unclicked Scale Cursor Proportionately. A day later, the mouse froze again, and I went into the AI preferences, clicked Scale Cursor Proportiantely, went to my document and it didn't work. I went back into Preferences and unclicked Scale Cursor and it worked! I've had to do this every time I open up a document after having quit out of AI.
While I'm happy I'm able to solve this on my own for now, I don't understand why this issue is happening and would love to be enlightened about the cause.