Greetings, Terwilf!
May I ask, did you tie the game with your itch.io account when you purchased it? If not, then the game will not be presented in the "My Purchases" section in your itch.io account, and you might not be able to access the download page.
To solve this, you could refer to this article to retrieve the link for the download page from itch: https://itch.io/docs/buying/already-bought.
You could also search your email inbox and see if you could find the link sent by itch by the time you purchased it.
Received the "Redeem Your Steam Key" email means you are one of the key owners, I can confirm. And I have submitted sufficient Steam Keys for all the key owners. No worries.