No. Your Guardian only sees your device's protection status, never your files, browsing, or screen, unless you invite them in for a specific Family Support session.
What this means
Your Guardian's dashboard shows whether your device is protected and when it was last checked, nothing more. If you turn on Family Support, they can look at your screen with you, but only after you tap Allow for that specific session, and you can stop it anytime. See What is Family Support and how does it work? for the full picture.