Sleep is not just "reduced" cognition, it is an entirely different state all together. In sleep thalamus becomes a gatekeeper that makes sure that stimuli cannot get through (although the important ones still do, like a baby cry will nearly always awaken a mother, even a faint cry will do). So, again, it is more radical than "quiet wakefulness" due to exhaustion.

Now, with "lower" animals it gets tricky, because all we have is a behavioral definition of sleep. But still, it makes a distinction of reduced awareness, arousal latency. Can we call it "sleep" in these animals, jellies included? Maybe not, maybe it is some sort of proto-sleep state?

I'm not convinced because your answer doesn't address the nervous activity of these lower animals. Maybe they don't exhibit any at all in that state, but there's no reason to preclude this diffuse, sparse network from exhibiting patterns exhibiting precursors to sleep comparable to at least one of the human sleep phases.

Yes, it's getting interesting. There are probably significant differences in chemical activity in cells that could be quantified and strictly detect in which state the organism is in.