Ah I see where your confusion comes from. Both in chemistry and in geology/energy, an extraction is a process in which there is no alteration to the chemical structure of the molecules, the molecules are just recovered from a different phase/embedding matrix. See e.g. https://en.m.wikipedia.org/wiki/Extraction_(chemistry)

In this case, we talk about hydrogen as a shortcut for dihydrogen, not for hydrogen atoms. To get H2 from H2O, you do an (electro)chemical transformation. The process is just referred to as water electrolysis or generation of hydrogen by electrolysis, but in no way as an extraction, as that would imply there is already H2 is the starting material and you just recover it. Like if there were natural deposits of H2 rich minerals or liquids and we extract from there, which is not the case. Cheers!