Does the school have access to email content of my personal email if logged into Chrome with my school account?

Does the school have access to email content of my personal email if logged into Chrome with my school account?

I sent an email to somebody with my personal email account (not my school email account). However, when using my personal email, I am doing it with a Chrome browser that I am logged in to using my school account. Can the school know who I am messaging and the content of that message? I did not turn on sync.