The world itself is anarchistic. Each counties has its rules but international politics have no governing body (the UN doesn't really rule over every state, just serve to mediate discussion). The country with the biggest stick would probably be the US, but they haven't conquered Canada or Mexico, let alone everyone else. Other players like Russia or China have influence too.

While the US does have a lot of soft power in influencing nations, they certainly aren't making the rules for other countries and puppeting them.

That's why anarchy isn't stable, it's a state between governments but eventually some kind of rule will emerge, and you're correct in that "bigger stick" is likely to be the first.

Generally, it's envisioned as being a lot like now, but with no classes, and people making and remaking the rules on the fly rather than having set laws and set authorities. No laws, no government, but not no rules.

We have a better word for that. Dictatorship.

I feel this is relevant:

...proponents of communism have postulated that within the new society of pure communism and the social conditions therein, a New Man and New Woman would develop with qualities reflecting surrounding circumstances of post-scarcity and unprecedented scientific developmen ... Among the major traits of a new Soviet man was selfless collectivism. The selfless new man was willing to sacrifice his life for good causes ...

https://en.wikipedia.org/wiki/New_Soviet_man#Selflessness

Of course, arguably the soviet project failed to this new man, so much so that 'homo Sovieticus' is now a pejorative:

Homo Sovieticus (cod Latin for 'Soviet Man') is a pejorative term coined to describe the average conformist individual in the Soviet Union and other Eastern Bloc countries. Popularized by Soviet writer Aleksandr Zinovyev, it gained negative connotations and represented the perceived outcome of Soviet policies. ... Homo Sovieticus (cod Latin for 'Soviet Man') is a pejorative term coined to describe the average conformist individual in the Soviet Union and other Eastern Bloc countries. ... Characteristics of Homo Sovieticus included indifference to work results, lack of initiative, indifference to common property, chauvinism, obedience to government, and a tendency to drink heavily. ... traits like indifference, theft, lack of initiative, and submission to authority ... Some argued that the disappointment of intellectuals in the Soviet project had negative consequences, contributing to elitism and an anti-populist stance.

https://en.wikipedia.org/wiki/Homo_Sovieticus

Anarchy is generally assumes that people will naturally cooperate without arbitrary distinctions. In practice most anarchists are mostly anti centralization. The smaller the political entities are the better (singular persons if you take it to the extremes).

Imaginary utopias remain imaginary. Anarchy is whomever is willing to brutalize others the most rules until someone worse comes along.