My school has provided us some emails with a custom domain (not @gmail.com but @myschool.smth) and we as students are only able to login via gmail, however i obviously do not want that. What can i do to prevent that? I tried logging into the email via Thunderbird but i get blocked because my administrator doesn’t allow that.


Sure. But don’t forget to take steps to prevent Google from harvesting your non-school data anyway. If using an official Gmail app, you’re probably screwed; they get your location, wifi, device info, why not?
If using a web browser, be sure it’s a privacy-focused one, don’t sign into anything but Gmail, and sign out and close the browser completely every time to clear cached data. And Google will still scan every email with automated scrapers, potentially training their AI on your carefully written essays, etc.