Similar discussion: https://www.reddit.com/r/degoogle/comments/i7vaq8/how_can_i_degoogle_at_school/
Anyway, if you want maximal compartmentalisation between your school identity & the rest of your life:
- Treat school Gmail as read-only, as far as possible: write & send only if absolutely necessary & be concise.
- Use browser compartmentalisation as others have recommended, or if you have time on your hands then go a step further & use Qubes.