To my knowledge, the Star Trek universe hasn’t really gone into great depth with regard to how money is handled. Picard gives a general idea in First Contact, but it could be just setting the mood for when Alfre Woodard’s character calls him out on his so-called “enlightened sensibilities” at the end of the movie.
Also, just because there is no “money”, doesn’t necessarily mean there isn’t some other method of exchange. In the TV series the Ferengi used latinum as a valuable commodity for exchange and it’s safe to assume that Federation crewmembers vacationing on Risa or some exotic locale which isn’t a member of the Federation may require some type of currency.
In the first episode of TNG (Encounter at Farpoint) you see crewmembers shopping for fabric but there isn’t a mention of how that exchange is carried out.
I think in the original series “credits” were used as a currency. Trader Cyrano Jones quotes prices in credits in The Trouble with Tribbles. Of course, in that episode, the Tribbles blew up the supply/demand curve.
Star Fleet credits...they’re mentioned many places. You can’t have an economy without some form of money, it just doesn’t work. What about “dirty” jobs and grunt work, it all still exists in the ST universe...without currency there is no motivation to do this kind of work...”self betterment and improving the human race” doesn’t cut it.
I take it with replicator technology, commodities, food and shelter are taken care of but if you want the luxuries like Scotty’s retirement boat, you need credits.