There are rumours of a Steam Cloud [0]
IMO this would be the best of both worlds. I don't want to purchase games from Google that will only work on Stadia. The ideal solution is to purchase games on Steam that you can play either on a regular PC, or on Steam's Cloud Gaming Service. I'm fine to pay $5-10/mo for Steam Cloud, but I really, really don't want to re-purchase some games again (like I'd have to do with Google), or lose my cloud purchases if either a) Google cancels Stadia, or b) I want to switch to a different cloud.
[0]: https://www.resetera.com/threads/rumor-valve-is-working-on-s...