Scotty says he “bought” a boat at one point, but I’ve also seen long explanations that “bought” doesn’t necessarily mean with money and it’s just a common Human expression for when you get something.

I think it’s clear that on Federation worlds you can just rock up to a replicator and get anything that isn’t dangerous (and you can get the dangerous stuff with the right license/permit), but on the frontier/border areas (ie DS9) Federation citizens receive a stipend or a wage so that they can live “on the economy” along with the non-Federation citizens.