If you've used GFN, then you know that most game use Steam Cloud so your saves aren't locked in. Stadia has also claimed they let you export your save files.
Except it's notoriously flaky. I've lost several save games and support has said everything from I'm lying, it's my router, and ghosting me. Can't use a provider that doesn't take data protection seriously.
That's strange. Do you properly shutdown the game and wait for it to sync before closing the instance?