Even full state authority does not eliminate markets, it simply changes the participation. A lot of internet Communists get this wrong. Marx is pretty clear that the state only withers away when there is no more material scarcity. Unfortunately, instead of actually working towards that endpoint, we are stuck endlessly relitigating whether or not implementing a brutal dictatorship is a good way to liberate workers.

There are non capitalistic economic systems that are also don't require state ownership and are non authoritarian. Literally just incentivizing worker owned coops is an example of how you can drastically shift the economic system without changing the political system. Markets =/= capitalism. The ability to hoard capital and thus power through private ownership is capitalism. I'm not saying that what i described is the perfect system, it's just an example of something possible outside of your argument.

the complete authority over all labor and markets it likely isn’t a very free nation, and all authoritarian nations also devolve into castes almost immediately with no recourse to push back.

Yes, that's an ok description of current reality under capitalism.

Capitalism cannot exist without a state ensuring the ruling class keeps being able to exploit the working class.

Otherwise, who secures land claims? Or other private property from being taken by the working class?