Mine do “sleep” in every sense of the word except for closing their eyes (because they can’t). I have a tank full of African cichlids, and if you go in the room at night after the lights are off for the evening, they’re all bedded down. Most of them will actually be resting on the bottom, or on a rock or piece of driftwood, often nestled into a cozy spot. Others will be just floating but stationary. They’re clearly in a deep rest.
I’ve noticed that the older fish will nap during the day, usually in the same place, such as a nice depression in the driftwood. They’ll be lying there quietly until you walk by and disturb them. Unfortunately I’ve noticed that this daytime napping is a sign that the fish is quite old and won’t around much longer.