My high school gave us student Google accounts which we have to use at home to access our homework. Is it legal for them to track our web searches when logged into the account away from school?

Basically what the title says. At the beginning of this year, the school system assigned us Google accounts. We have to use these Google accounts away from school to sign in and access our homework, at home. I always try to log into it in an incognito tab because I'm paranoid.

Sometimes, however, I'm forget to log off of the account and end up logging into social media and searching things I wouldn't necessarily want the school to know about. Nothing illegal -- just stuff I find to be none of their business. Could the school legally be keeping track of history on the account even when I'm logged with it away from school?