Using a dedicated browser should be good enough. Since you might need some proprietary google stuff, I'd suggest chromium portable, that way once the class is over, you can simply delete the whole folder and call it a day.
I have the same issue. My workplace uses Google to store their documents which need to be accessed on a daily basis. I use Firefox for my personal web browsing and Brave for Google or work related stuff. Isolating Google/work stuff from my personal browsing has been working for me. I also use Thunderbird if I only need to open or send an email via Google. Brave has ad and telemetry blocking options and you can (for now) still use Ublock origin.
Keep in mind Google Workspace has a significantly different privacy policy to Gmail and other consumer services. Data is not used for advertising purposes and is owned by you. They also warn you if you leave to a consumer service like YouTube.
Best bet would be to simply have a separate browser you're not logged into your account with. Don't do personal browsing with a company owned/educationally owned institution device.
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