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AFAIK. Renpy should have both local and global (central) save folders on all platforms.

Local being in the game directory and the global directory should have save folders of every single game (on Windows AppData\Roaming\RenPy).

On Linux the global directory should be ~/.renpy/game_directory.

BTW. If you ever want to nuke saves for a game, you need to delete both the local and global save folders for that game.