I think it shows that people yearn for power and control over others just look at all the karens, the reddit mods (you know which kind), the trolls, supporters of certain parties and so on.

I think that's way too generalized. "The internet" paints a very distorted picture picture. First, the absolut vast majority of people online are lurkers, so you don't see what they think or do at all. "Nuanced takes" barely exist because people just blast whatever is on their mind right now into the void that is then interpreted by millions of differently biased people.

The mods, trolls, etc. are the fringe of the fringe, often the types of people who have no real life, who cannot really fit into society and who have to find other ways to get attention/validation.

Mods aren't some kind of villanous power hungry monsters, they are socially untalented nerds who want to do something that feels important, but who often feel unthanked, underappreciated and feel as if everything they do is wrong no matter what they do and who have to deal with the worst of the worst on the internet constantly. And then they are expected to have a discussion about every second decision they make because somebody feels that their comment was not interpreted the way it was intended and cries censurship if the discussion is blocked.

Given that it is somehow expected that moderation often happens without compensation (even though it is essential to a community), I'm suprised it even works as well as it does. If people in general were as powerhungry as you seem to make it out to be, people would kill for the chance to become a mod. In reality, the absolute vast majority of people doesn't even think about it, which means the job is left those who probably having human interactions in the first place.

I guess they imagine that extremist regimes will provide them with that power

Most don't think too much about that stuff (or anything really) in the first place. Many "right wingers" aren't like the disturbed "true believers" you see at rallys or stuff like that, for many it's just the community aspect they crave and the rest is no mostly larping.