What does it mean for workers to collectively own means of production? Am I supposed to own only the laboratory I work at or everything everywhere? What if I decide to change a place of employment? Why doesn't owning it though the intermediary of the state and your representative in the communist party qualify?
It sounds like the exact opposite. Nationalizing production sounds like the building up of the state. What am I missing?
Good question!
The "state," as defined in Marxism, is the "mediator of class antagonisms". With no class, there is no state (and thus we would say primitive communism was also roughly stateless) even if there is still a "government". Without class antagonisms driving political conflict, the government is predicted to become essentially a managerial apparatus.
You are right though that if we speak in liberal parlance, building up the public sector until there is no private sector would be considered growing the state, as it is certainly expanding what falls under the control of the government -- which in turn is controlled by the people through democratic means without interference from an owning class that is distinct from the rest of the population.
It's like how "state" and "nation" are also taken as synonyms most of the time but have somewhat different meanings even in liberal parlance, as evidenced by the need for the term "nation-state". "Nation" is more of a cultural descriptor, in its more technical sense, which is also why fascists love to use that specific term so much.
Thank you. Are there any primary sources you can refer to explore this topic more?
The main thing I'm going off of there is State and Revolution, along with Socialism: Utopian and Scientific to a lesser degree.