The itch.io version of the game doesn't come with a steam key iirc. You'll have to purchase the game again but on steam instead if you want to get it there.
HafuWeeaboo
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I'm guessing that they may have downloaded the game via browser (or not with the big red install button while on the itch app) and supported the game while it was free by giving some additional contributions?? If downloading on browser, a pop-up does show the optional "This game is free but the developer accepts your support by letting you pay what you think is fair for the game." choice, and doing so likely made itch think that you bought the game whether or not it was free, depending on how much was contributed at the time.
That happened to me when I paid for the DLC expansion on A Date With Death when the main game itself is free.
Hi yes, it was free to play up to Episode 8, before 9's release.
But they explained in their latest monthly public Patreon newsletter about how having a price on it would help them in putting extra work into making the last episode and epilogue in having the best ending that it'll get.
It's a pretty understandable thing for a lot of Visual Novel games to do as it grows with each new update and features. :)