That's interesting. I have a vague memory 10+ years back of that same thing happening on the PS1 original.

Unfortunately, off the top of my head, I don't think it saves too much time (At the moment). On my current routing, The 2nd H key is used to unlock the catapult to Sparta (Which leads to a quick way to get fire spears > hydra, and also to leave Egypt otherwise you have to go amazons > Athena and then double back.. to Sparta). You get this key via traversing back to the Lamias room with the P key for lipstick. This takes less than a minute (~45s?) detour after picking up the passwords and on the way back from Egypt. It'll take 1.5-2 minutes to get the cow back to Hera for another H key if I'm reading this right.

Of course, there could be something else found from this but at the moment I don't see it being too beneficial.