I think by public here you mean “state” ownership. Socialists believe in workers owning the means of production.
So like, every co-op, worker-owned company, and software company is socialist since their workers own the means of production?
Also, couldn’t you say that if the workers control the state, (i.e. through a democracy) that they own the “means of production”? Or does socialism have a requirement for more direct ownership?
Worker co-ops are probably the closest thing to a glimpse of a socialist workplace under capitalism, yes, but unfortunately these companies must exist in a capitalist economy. This means they still must compete against profit-driven companies and do things that are not in the interests of their workers in order to stay afloat. If you’re interested in learning more about how this directly related to socialism, I recommend this article: https://monthlyreview.org/2015/02/01/cooperatives-on-the-path-to-socialism/.
To your other question, the answer is no. Under a capitalist framework, corporations (the ruling class in Marxist terms) own the means of production in that they are the primary owners of private propery (the factories, machines, offices, etc that produce goods and services). They take the profit that workers generate and keep it for themselves - it isn’t distributed back to the workers. Just because the US is democratic does not mean the workers own this private property or have a say in how it is used.
