Plants physiology changes significantly during the night, so it's not just "no more photosyntheses without Sun"... respiration rates at night are strongly correlated with the amount of stored carbon and sucrose in the leaf tissue, which is probably related to the fact that plants also grow faster at night.

Maybe not.

Plants have two sources of nutrition: uptake via their roots and photosynthesis. My general understanding is that photosynthesis is what provides them energy whereas uptake via roots provides water and some essential nutrients they can't synthesize.

The details will vary and some plants, for example, grow in total darkness or feed parasitically on other plants. But I think photosynthesis is roughly the equivalent of humans eating carbs for energy.

So it's a little like saying "One defining characteristic of sleep is that animals stop eating." And, in fact, hibernation through the winter when food is in very limited supply is a known mechanism of survival for some species in harsh climates: They sleep instead of eating.

In fact, my understanding is that to some degree eating and sleeping are substitutable. If you can't sleep, you can eat to help keep yourself functional while awake on a long shift.

I think they do this on episodes of Deadliest Catch: feed people more when they are pulling a long shift and going to be awake for 24 hours straight.

Well, you raise a non-trivial point that is more than just a semantic issue, viz what do we mean by "sleep"?