I think a streaming service with a Linux backend is more likely than another Steam machine push.
One of the biggest problems with Stadia and the like is that you have to buy another copy of the game whereas Steam already knows what you own and will let you play it locally.
Strictly speaking, Stadia is "a streaming service with a Linux backend", but I think Steam could do it better than how Google's gone about it. The issue would be that Valve would need to renegotiate it's distribution deals to include streaming rights in addition to providing user downloads, and many publishers would drag their feet on allowing that, based on how publishers made noise and opted out of nVidia's Windows-based offering.
But a service that offers my Steam library via cloud streaming would be a very tempting offering.
Interesting. I wonder if Valve is building this so third parties can do the capital-intensive work of building up/out hardware (given that they're listing GeForce NOW as the only supported client), or if they're also intending to enter the market themselves.
One of the biggest problems with Stadia and the like is that you have to buy another copy of the game whereas Steam already knows what you own and will let you play it locally.