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.
I only caught it this last time I watched it from start to finish because I, too, had questioned how they pay for stuff. I mean, the holodeck they have allotted time for which was part of the deal Sisko made to keep Quark on the station for morale (and info), but they also drink at the bar and play Dabo. Those definitely couldn’t be just gratis lol