Well, so am I.
At least, that’s what my degree shows.
Again, as I stated, H2 does not exist in that state in any quantities on Earth. Sure, it may be common in the universe, but on Earth almost every hydrogen atom is chemically bonded to other elements.
It takes ENERGY to release the hydrogen. Then, when you let the hydrogen recombine, you can get energy out of that reaction.
EXAMPLE: H2O can be cracked into hydrogen and oxygen by electrolysis, as you mention. That take…ENERGY. When hydrogen is burned in an oxygen atmosphere …yep, heat and WATER are the byproducts.
Again…H2 should be considered as a battery. It is a store of potential energy, but it takes energy to create the H2 molecule from its source. (Usually hydrocarbons. Lol.)