There are capitalist elements. The Picard family still owns a farm and farm house and pass it down generations. There is still some concept of money being used by humans who are pursing payments for rare and stolen goods. Most of what we see around Starfleet is merit driven people working in starfleet out of self interest but the ships appear to be owned by Starfleet and they seem to have some democractic structure. Since most basic needs are met via replicators it seems they are post scarcity and trips to the doctors seem free but is not really socialism in the sense of people owning the means of production, there doesn't seem to be much of anything said about how these ships get built and the implication is its a lot of automation but there seem to be a lot of facilities on Earth with people in them like Starfleet academy and in bars. We have no idea how factories work in this world other than on other planets and people work in them.

I don't think its brilliantly clear, there are a mix of ideologies on display and what makes it hang together is the humans are all behaving well, which isn't very human nature like at all. People don't seem to own what they are working with in all cases but they do in some of the smaller settlements so its a bit of a mix dependent on circumstances.