Even if you’re using a personal computer, I think a policy like “while in class (during distance learning or if you bring your personal computer to school) or while taking a test you must use Chrome, be logged in to your school account, and have the GoGuardian app enabled” is totally reasonable. So is making it so students cannot use a school Chromebook without being logged in to their account.
Forcing students to install and run GoGuardian while outside of class on a personal computer is not OK, bit I’ve also never heard of a school that requires this.