To my knowledge the federation is completely post monetary. But, we do see individual people who in it that use money. Riker mentioned a few times owing debts or being owed debts from card games and the like, iirc. I think it’s largely a personal choice, as money is unnecessary in their society. Nothing that matters has a monetary cost, like shelter, food, etc. And luxuries within the federation itself seem to also be free at the point of use, but I think there is some kind of credit system in use. Sisko mentions using up a months worth of transporter credits to come home for dinner during his time at the academy, if I’m remembering right.
Given the whole schtick of being a post capitalist, but not quite fully communist, society that the franchise has, combined with my personal knowledge of various socialist ideas around transitionary societies, my best guess is that they function off a form of labor voucher. Non transferable credits to be used for whatever goods are restricted or scarce. But with some kind of loophole around the transferability when it comes to dealing with non federation members who still use money.
I’m sorry, you’re all crazy people who are wrong with your wrongheaded wrongness. Ent is second best 90s/aughts trek. This is a factual fact that is true and good in the eyes of the Lord and Prophet Rodenberry, peace be upon him.
Loudly sings Faith of the Heart over any counter argument