If I tell you to get the fuck out of my way I also regulate population but I’m not the state.

Regulate would mean a legal basis to dictate/legislate to.

Note that even your definition says ‘a’, not ‘the’.

You're going to have to be a bit more specific than that, there are a lot of "a"s

Also, and more importantly, enslaved people are seen as property (and thus also as means of production) instead of population.

Yes, that is how they were seen by some people. And those people were wrong. If I become a tyrant and declare I'm the only real person and everyone else is my property, then seize all their property- is that capitalism? Because 1 person just owns all the property? No, its because the definition of person is wrong. Enslaved people were still people, so they could not be property, even though the law claimed they could be.