Hi there. I just wanted to inform that something was indeed amiss and support managed to get a solution. I got my steam key working now.
Thanks!
So I've sent itch.io an email asking about the situation and what to do. They do have a link (this one: https://itch.io/docs/buying/already-bought) where you can see how to get the steam key and the solutions for it. They didn't answered yet (tho they do say that itch.io doesn't solve problems for specific creators or something like that).
The key is still nowhere to be found, but I guess I'll wait and see if they do answer and provide a solution.