I'm sorry. I'm at a loss, my friend. 🤔
You might see if you can pair the mouse while you have the Mac booted in Safe mode. It may take longer to safe boot (5 min) so be patient.
How to use safe mode on your Mac - Apple Support
Safe mode will often correct weird software behavior by forcing the OS to do disk repair, clear caches and other housekeeping and disables acceleration and third-party mods. When you're in safe boot, the machine won’t be at its best performance, especially with graphics, but that's expected.
Can you coax the mouse to pair in Safe mode?
Exit safe mode by restarting your Mac normally and evaluate the issue again.