I fail to see how what I said conflicts with any of what you said.

I think the differences are subtle but meaningful. I think another way to interpret "communism" in the Marxist sense is "anarchy" meaning there's no central deciding body.

Communism takes this idea and applies it to all companies in all industries. ie, the government has oversight on all companies.

This is different from what I mentioned in my post.

He theorized that eventually we will realize that the capitalist machinery(including the government, borders and nations) must be shuddered in order to truly free everyone.

I did forget to mention that there would also be no money. And there is no government to oversee all these industries. (I understand that in our capitalist world this sounds like libertarianism, but without money there's no profit motive).

how does a society theoretically operate under communism?

Marx doesn't actually postulate what this might look like, but one of my favorite sci fi authors ever did. In Ursula K Le Guin's brilliant novel "The Dispossessed" she imagines what a truly communist society might look like. I highly recommend it if you'd like to see what she thinks it might look like.

But just a a brief description (which doesn't really do it justice). There's no government. The main character is a scientist who works with the university as a collective. Students and teachers have ad hoc discussions about what classes might be interesting to have. Farmers collectives post requests for work during harvesting season. Kitchens request help to areas where they need help. Everyone has some skills and has a culturally ingrained belief that they should help the whole group. They also believe that everyone is equal and nobody should hold power over other people. Nobody is paid for the work but they all see each other as brothers and sisters and so working is something you do, like when your parents ask you do to yard work while one parent cooks and the other parent fixes the car. (This is simplified from the book, I don't think it truly captures the whole of it).

Thanks for your comment, I appreciate our conversation.