To begin with, Google Workspace =/= Google Gmail, so the privacy considerations are completely different.
With regards to privacy concerns, your school knows: every IP address you log into your email from, user agent that accesses your email (i.e., they know what client you’re using), and every email that goes in and out of your student email only, any sites/apps that use Google SSO that you log into with your student email.
Google knows: your school has registered another user to their Workspace license, anything your school knows (but only technically, I wouldn’t expect Google to be snooping on every Workspace user)
So tl;dr it’s not gmail it’s a corporate product and I would only really try to aim for compartmentalising because it’s personal vs school stuff, not because google is going to snoop on every bit of data on your devices (because they can’t)