It is possible for players who played Cyberpunk 2077 on Stadia to transfer their save files to PC before the service shuts down. To get the files, you have to manually download your data from the internet and bring it to your PC.
There is a new support document detailing how it works. If you want to carry your progress over, you should do it as quickly as possible. CD Projekt Red's global PR director said that once Stadia shuts down, you won't be able to retrieve that save.
If you bring your save files to the PC, you can use them with Cyberpunk 2077's cross-progression feature, which means you can carry over your Stadia save files to console. You have to own multiple copies of the game, but if you really want to play your Stadia character on PS5 you can do it with a little work.
The Takeout option is not the most elegant solution, but it is nice that you have the option to keep playing.
Like the rest of us, developers were shocked by the sudden announcement that Stadia would be shutting down, and they've had to work quickly to respond to players wondering what might happen with their games and progress IO Interactive hopes to have a solution for Stadia customers by the end of the year.