All I can say is, I grew up in the 80s and that means no internet.
I come from a working class family.
The neighbor was an architect who had a C64. Because of that I got interested in computers at the age of 8.
Age 10 my dad bought me a CPC 464.
I learned that BASIC and wrote a graph that displayed a static set of numbers, kind of a stock exchange graph. I had a deal with my dad that he'd pay me if I managed to write this and complete it. He paid.
Later I got a C64 because of games. Also the Final Cartridge 1.
It had the ability to freeze execution, a memory monitor and assembler editor.
I cracked my 1st game at the age of 11. One year later I wrote cracktros and linked them with my cracked games.
I also used it to cheat in games.
However I never did professional piracy. I only distributed the disks locally among friends.
It was really amazing seeing one of my cracktros years later at someone's C64, a guy I never knew.

Nowadays the playing field is different.
The internet isn't real life. I have never witnessed such hostility in real life that I have on the internet. But it is now part of life. And it's full of junk.
But you can't shield your kid from it.
It will have to deal with it sooner or later.
But... I still had a somewhat normal childhood, exploring nature, building tree houses and such. If your kid spends all its time in front of a screen, it will never experience or learn about the real reality, not the fake interreality.
Already the rudeness of the internet is changing real life.
Because people get used to be rude because they're sheltered from repercussions on the net, but get used to that behavior in rl.

To make it short, I was not supervised or monitored. I had great grades in school without learning. Just listening to what the teachers had to say was enough to make it through school with an American B result in the end, without ever learning for a single test.
I would've liked if my parents pushed me a little bit. That B could've been an A if I tried.
But I really enjoyed my freedom and when the internet came 1995 I enjoyed the freedom I had there.
The internet was something that wasn't on the mainstream people's radar. It was my refugee from real life and its harsh, controlling rules. Over the years it turned into this trashpile that's the complete opposite of what it was. It's now used to spy on you and to monitor you and everyone. What was once a dream of freedom and progress is now a tool for oppression and used to spread nationalism and racism or let's put it like that... reality has caught up with it and made it part of its ecosystem only without the barriers of decent behavior toward each other. But then again it's just a medium.
The way I live my life and have lived it in the past 25 years was like a slave, sitting in front of a computer screen writing things in a made up world, because I need to earn money to live or rather to perpetuate this slave existence.

I often wonder if I had a child what I would teach it in regards to the internet. Probably that it can be a dangerous place, just like the real world.
I would not prohibit its use or have dedicated "screen time".
But I would not allow purchases. If they manage to make their own money in it, of course they could spend it any way they want.
I would urge them to go outside and play vs spending time in front of the computer. Nowadays you have your computer with you.
I would explain why, with every decision I do, so the kid understands why I do what I do and why it should as well.
And sometimes I would have to be the authority, because that's life.

My dad said once, "I don't want to be your dad, but a friend". That is not what I wanted. I wanted a dad, friends I could always have, but only 1 dad. I think he said that so it was easier for him to accept his role. I'm not good with kids either or other people. When I was younger I hated chit chat or smalltalk. Most jokes were not funny to me. I always admired Mr. Spock for being cold and logical. When things wouldn't go my way instead of having emotional outbursts, like it did when I was younger I would get cold and robot like and express my disagreement that way.
So yeah, of course play with the kid if that's what makes you happy, because if you do it only because you think it's good for the kid, then it's superficial and bad for both.
In the end it's just another human, so what do you do with other humans? With your child you have more in common than with other humans. It learns from you, copies you, your good and your bad.
Whatever you do, be honest.
No, never mess with them and their friends. They're theirs friends, their relationships, not yours.
Of course if you see something that is not ok, talk about it.
In the end you're the parent.

Communication is everything. Talk talk talk. Remember when you were young? Spot stressing about it and just go with it.