Something seems to have gone very wrong here already. How come we don't have an e-pawn? I feel like you must have exchanged on c6 and then taken on e5, in which case you are the one disregarding opening theory.
Ruy Lopez

Wait, you're Black. I was confused by the board orientation and also by how you said "Black totally disregarded opening theory", you meant White there.
Anyway, the engine's suggestion of h5 does make sense when you see it, but what I'd play here is Bc5. I'd like the bishop on d6 but White will just attack it with a knight at some point, it's still on a nice square on c5 and looks more secure, it also obviously discourages f4. I want to play Ne7 not Nf6 because the knight kind of looks in the way to me there.

Can you understand my frustration? Black played the opening in a way that goes against opening theory, as how not to play. And yet, black got into a decent position.

Stockfish 16 evaluates this as like -1.2 at a high depth, which means it thinks this has a better than 50% chance of being a lost position for White. You can't hope for much better than that as Black just from the opponent playing a sloppy opening. It's not super easy to find the right ideas as Black, but that goes for lots of positions where the opponent makes mistakes.
What should black play? I played Nf6 and white responded with f4, which was annoying. What upsets me about this game was how black totally disregarded opening theory and still managed to get into a decent position.