The link says we can find it in my purchase page but there is no such "claim key" button you were talking about.
Below is my purchase page.
Oh, my bad, it's said you got it in January.
It's weird it doesn't show up for you, cuz I can see how other players activate their keys.
You can text me on discord or find the purchase email from itch. I think the claim button will be there.
That's what Itch says about the keys, and there're enough keys stored on the platform: 