Under circumstances of low oxygen, aerobic eukaryotes can switch to glycolytic metabolism. Humans can do this too, temporarily.
Glycolysis is an oxygen-independent metabolic pathway. The wide
occurrence of glycolysis indicates that it is an ancient metabolic
pathway. Indeed, the reactions that constitute glycolysis and its
parallel pathway, the pentose phosphate pathway, occur metal-catalyzed
under the oxygen-free conditions of the Archean oceans, also in the
absence of enzymes.
Anaerobic glycolysis is less efficient than aerobic, yielding a third of the energy per glucose molecule. Also there are byproducts that must be dispensed with or regenerated to glucose; lactic acid and ethanol are examples.
Maybe the original plants used glycolysis back when they could make sugar but were not assured of plentiful oxygen. They can still do it today.
Low Oxygen Response Mechanisms in Green Organisms
Low oxygen stress often occurs during the life of green organisms,
mostly due to the environmental conditions affecting oxygen
availability. Both plants and algae respond to low oxygen by resetting
their metabolism. The shift from mitochondrial respiration to
fermentation is the hallmark of anaerobic metabolism in most
organisms. This involves a modified carbohydrate metabolism coupled
with glycolysis and fermentation.
So your plants would be glycolytic. That is totally legit biochemistry and not fiction. For a fiction I like the idea that they store the end product as either ethanol or lactic acid, regenerating sugar from it when there is lots of water and sun to use. Those plants might be harvested for their storage products in addition to their sugars.
It occurs to me that plants in a low oxygen environment might store the oxygen they produce in their tissues, just as they store the carbohydrate product. Gaseous oxygen is reactive and difficult to store though could be stored as bubbles in an aquatic plant.
Animals store oxygen using heme molecules. Hemoglobin is one. Myoglobin stores large amounts of oxygen that whales use during their deep dives. Your plants could have similar pigments that capture the oxygen product of photosynthesis and keep it handy for aerobic metabolism when needed.