As a lot of people here are saying, education is alpha omega. However, what makes or breaks this education (whether they end up starting to "test" this education), is how you present it:

Saying casually "You're not allowed to go to these websites because I say so." is like inviting them to explore anyways, and try and find out for themselves whether it's as bad as you say or not (because their classmates have gone to these sites after all, and they're fine).

Instead, make sure to tell them why you're doing it is because you yourself don't even go there, because of X serious reason. Be it big tech spying on and manipulating you, risks of implication in illegal activities, getting scammed, or psychological trauma of seeing too much. Perhaps refer them to a documentary that explains your point, so that you're not the sole source of trust.

The internet is a dangerous place, and that should be communicated from a person who genuinely thinks so themselves (the parent).

This is not to say that the internet can also be useful, but only if used correctly. As for guardrails that can prevent accidentally ending up in the wrong place can indeed be as others mention here, family mode, blocklist, safe DNS, etc.. It's not there to restrict them, but to safeguard them (and you).

Make sure you're also a safe person to talk to about taboo topics. Things like sex, porn, suicide, hacking, gore, drugs, war crimes, school shootings, and various illegal activities should all be safe for them to seek you out as the first point of contact. NOT the internet!

The best monitoring tool I can recommend for a child is for them to feel safe in self-reporting.