Risa

The whole idea of Replicators and Transporters is that they have some technology which can efficiently convert matter and energy, so it's possible that they use some sort of reverse-replicator to process waste.

You also never see what they do with the glass cups the replicators create when someone asks for a drink...

By the 32nd Century, it is confirmed canon that human waste is directly reused for food replicators. "It's pretty good for shit." - Admiral Vance

It's less clear whether that's true for earlier eras or not, but the existence of "matter recyclers" sure implies it.

But all this still doesn't address the matter of where people poop on a starship.

Surely the bridge crew all have their own freshers, but what about the lower decks? Do they have communal restrooms? What about accomodations for different species needs? Is there a diplomatic lounge with a wide variety of bathrooms available? When they have guests from a different species they're not familiar with, is there an ensign whose job it is to research that culture's bathroom customs and ensure they have the appropriate facilities replicated and constructed? Is there maybe a small holodeck reserved for this purpose? These questions need answers.