Aren’t you using up water to release hydrogen, which will release oxygen into the atmosphere. Does this not use more water than can be recombined from free hydrogen and oxygen. I am ignorant on this stuff, feel free to laugh or poke fun at me. It just seems logical.
If it "used more water," the water would have to go somewhere. Where could it go? Conservation of matter says that there's nowhere else, so the water in has to equal the water out. Of course, you're turning liquid water into water vapor ultimately, but the sun does that anyway.
I should point out that there would be some leakage of hydrogen. Some of that hydrogen would end up burning to water in the atmosphere, but most of it would probably just rise to the upper atmosphere and diffuse out into space. So, yes, in a real world system there would be some leakage of hydrogen and therefore some loss of water.