Since reducing atmospheric temperature is the primary purpose for burning hydrogen, creating water vapor exhaust, the most powerful green house gas, does not seem to fit into the real world equation.
Full disclosure - last chemistry class, almost 60 years ago.
As I think about it, that was almost exactly the same point in time when the French decided to go 100% nuclear, which still seems like a really good idea.
Sorry if, by not directly commenting on that, I may have seemed to be dismissing you - but the fact you cited is so obvious that I thought it didn't need my explicit affirmation.
We all know that a single molecule of H2O absorbs approx. 10 to 15 times as much incident infrared radiation from the Sun as a single molecule of CO2.
Water vapor is thus a far "more-deadly" (from the hysterical P.O.V. of climate catastrophists) greenhouse gas than carbon dioxide, molecule for molecule (and there is a lot more water vapor than carbon dioxide in the atmosphere!).
If you go to ChatGPT and try to "pick its brains" about this phenomenon, it will lead you on a merry chase, try to hem and haw, and do everything in its power to avoid conceding this fact, but if you keep dogging it, and formulate your questions very precisely, it will eventually have to admit it.
Regards,
Science class was a lot easier back in those days!

Regards,