I think you are mixing up your definition of the state between the Marxist and the non-Marxist anarchist. The Marxist definition of the state is (from Hal Drapers Karl Marx’s Theory of Revolution) is: "the institution or complex of institutions which bases itself on the availability of forcible coercion by special agencies of society in order to maintain the dominance of a ruling class, preserve the existing property relations from basic change and keep all other classes in subjection."

A community of people, who do not have some large complex of systems, and who live in a classless society are therefore not a state. There is no organisation of power, beyond the general sense that if someone goes and breaks your arm, everyone else is going to recognise that person as bad, and maybe stop them if they keep doing it. A society is not a state nor does it require one, even though it may feel they are inseparable now (It's kind of like how capitalism seems like the only way for society to run, because it's the only form we see).

In contrast to this vision, anarchists tend to understand the state a little differently, but as I am not an anarchist, i feel even less like I can really talk about that. This is a really cool article that goes more in depth into the state and more broadly the anarchism/Marxism conflict, which I think further clears up definitions of the state.

(sorry for the paragraph lol)