You don't necessarily* need to pay every time an update comes out. The game "Among Us" updates every once in a while, and you don't have to keep buying the game every time it happens. You just download the newer version, that's it. You don't lose access to your content, or they would very quickly end up in legal trouble.
I suggest buying the game on itch io because that version is DRM-free, and you don't have to worry about a multitude of problems when something is DRM-free, e.g. the problems that came with the Steam library update in 2019 and still exist to this day. If a game is DRM-free, it's just you and the game. You are also not forced to use the latest update either. All of that is why I suggest the itch io version.
*By "necessarily" I mean if the developer intends to publish a different version on Steam. It's rare, but does happen. The game "LIRE" is one such example. If you are not as massively against Steam as I am, then I suggest asking about the Steam version versus the itch io version on the "Saiko no Sutoka" discord.