I don't think you have to pay for every single update. It's a one time payment as far as I know (let me know if I'm wrong). I don't know about patreon, but if you buy it on itch io, you get a Steam key too if you message the dev on discord. If you supported it on patreon, then I wouldn't be surprised if you get a key (assuming you paid $4). Ask the dev on discord if you really did support this game prior to it becoming a paid game.
EDIT: the game page has changed since last I looked and now says "Anybody who ever donated previously with minimum amount $4 can get a steam key for FREE!" so I assume if you donated $4 via patreon, you will get a Steam key.