In TNG, Picard says that the Federation has evolved past a need for money. Indeed, we never see any.
In DS9 though, Quark talks a lot about bar tabs and costs. Surely O’Brien and Bashir don’t get free drinks, so how do they pay? I’d assume that any Ferengi worth his lobes won’t accept anything that can be replicated, so do Federation officers get a stipend of tradeable “value” when interacting with cultures that still expect payment?
I think there’s also a reference to Quark paying rent to Sisko for running the bar. Presumably that’s denominated in latinum. I wonder where it goes? Maybe the secret “Garak black ops” fund.
In TOS, at least, the Federation used credits and traders seemed to do quite well. In TNG and later, we see them barter for nearly everything.
WRT Quark in particular, I don’t remember him selling anything that wasn’t replicated. My head canon was always that Starfleet took care of the tab for those personnel who didn’t want to dabble in money as a hobby.