Tell me how to use iOS settings as secure accountability software

Or is the recommendation that it has to be a third party app? In which case, do any apps actually have the ability to monitor "sneaky" use of the phone to access untrackable content? I made the apparent mistake of getting my teenager an iPhone and it is not yet paid off or I would throw it right in the trash. How do I block ALL types of incognito mode, including YouTube and Google from WITHIN safari browser? I cannot use the "only allowed websites option" in screentime because that TRULY creates a massive daily inconvenience since a phone still needs to be used for the internet. Instead of mass blocking everything, I just want to know how to block or more importantly TRACK all internet usage. Both on wifi and data. If I have to go with a third party, I want to know straight up from apple what will not be accomplished so that I hopefully don't waste even more money, this is very stressful and frustrating