Prodigy makes it official. Starfleet ships have 'sonic toilets!' They make a flushing sound and you can apparently do something to break them by using them, at least if you're a Tellarite.

I can't help what happened in the show. Jankom used the bathroom and said he broke the sonic toilet. There was a flushing sound as he came out. Maybe it's a sort of holdover thing? Like it makes that sound to let you know that the waste is being removed, but it's a recording?

I wonder who was the first in the Federation who could successfully beam out their shit instead of going to the restroom.

Half flush, full flush, bidet. It's jot complicated.