I'm going to go against the grain slightly and say that it's not as bad as you might think. Schools and businesses have deals with Google when they pay for the software. Google is not allowed to scan everything to train Gemini the same way that they do for a personal free Google account.
That being said, it's always best practices to disconnect work/school and personal activities, for a wide variety of reasons. The more present threat is the work/school being able to see everything you do on the device. Like, EVERYTHING, sometimes even keystrokes. Furthermore, using your personal third party accounts will increase the attack surface by Google and your school/employer being able to associate the service and/or account with you. So at the end of the day, don't do anything personal on school/work devices, and you can't get burned by either party.