I use SQLite for game state management. It's just like any other database scenario. I write migrators that check the user_version of the database. It's just a for loop from user_version to current version. The migrators themselves can be arbitrary methods that sometimes modify game state to bring it up to date. The most common scenario is adding a new property to something, and then figuring out the appropriate defaults to assign for existing rows (typically null/0). But you can go all the way into the ETL rabbit hole.

I think the relational model via SQLite is the best way to manage state for the more complicated games like in the 4X and deck builder genres.