yes, at night they breath oxygen. Maybe they sleep during the day.

But their cells still consume oxygen during the day, don't they? In sunshine they produce more oxygen than they consume, but the cells are still fundamentally powered by mitochondria oxidizing glucose

Perhaps different regions of the plant "sleep" at different times? The plant has no need for high response synchronized behavior at all.

You still consume oxygen when sleeping.

Plants respire oxygen continually, day and night. It's a myth that they only respire at night.

Like every other organism except for anaerobes (mostly microbes, some fungi) they need oxygen in order to burn fuel for cellular processes. Plant cells are doing things day and night.

The origin of the myth is simply that they produce more oxygen via photosynthesis than they respire, and so are net producers of oxygen during the day.

yes, I meant net.

They need oxygen for the mitochondrial electron transport chain to produce ATP. The vast majority of multicellular organisms need oxygen for that reason, and I can count the exceptions on one or two hands (i.e. Pogonophoran tube worms, some anaerobic sponges, a few parasitic helminths).