I bought this game a year ago (and Itch says that it was acquired then) and played about half of it. I wanted to come back to the game and hopefully finish, but now I only seem to have access to the demo.  I also don't have a Steam key, although I gather I should have one.

[UPDATE] I seem to be able to access the game via the Itch website, but not the Itch client. Also, I've managed to get the Steam key so that's solved at least.

Same problem. Even if I go to My library through Explore in the itch app, clicking the download button on full Windows version brings up the app’s download window which only has one item in the drop down menu, which is Windows demo.

Not just this game, but a few, can't be downloaded through the itch.io launcher. (It's unfortunate, CrossCode is one of them.) If you download them manually from the website, you can get the game, the full game, as you own it.