You paid for the game on itch, the game on steam is another game, is not an update.
Besides Steam limit the amount of keys I can give for free, so I can't, I hope you understand.
It's not "really" another game let's be real. It's likely been made from the ground up but that's not different then any other developer. Lots of games have "overhauls" where it's remade from the ground up.
If you can't do it due to steam that's fine. However I find that odd. As a developer myself companies i've worked for have given out infinite keys. They usually just have to request more from steam.