Maybe we should focus on the rodenberry set of episodes. After all, he was the original visionary of the series and had, i think, a stranglehold on approval right up till a couple seasons into tng, were there any money related episodes of the original series or the first seasons of tng that would imply the federation, while providing all needed things for its people for free, also had a monetary system of some sort?
Another thing to keep in mind that further muddies the waters are the comments that would seem anachronistic like the "You're buying" line. That could imply that yes going out to eat dinner as opposed to getting something from the replicator costs money, but this culture also has a fascination with the past, as evidenced by the love of holodeck adventures from robin hood, film noir, sherlock holmes, etc etc etc. So they as a culture would likely still be aware of such lines and their meaning even if they dont directly apply. Sort of like how if I said fit as a fiddle you would get the reference despite not owning a fiddle. You're buying could as easily be a joke as they wander back to the replicators or a notification that they see it as a date as a legit statement that picard needs to pay for the food somehow. So we should probably stick to episodes where something actually happens that implies money is being earned by the federation somehow rather than offhand comments that could just as easily be cultural references to the past that have stuck around for various reasons.