If I'm understanding correctly, you're asking if you already own the game, you don't need to buy it again to play on Stadia? If yes, that's not the case. You will need to buy the game again. As for save (I assume that's what you meant by 'data'), it depends on the game. For example, Destiny 2 allow cross save, so if you can actually use the save data from other platforms to play on Stadia. Otherwise noted, you will not be able to use save data from other platforms.
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Stadia Guides are not employed by Google. Opinions are my own.
