No. But, you can run any store on them. Even access kde

Xbox and ps5 you're limited exclusively to their stores

Also, steam have done a lot to help all Linux gamers

Bazzite is basically an attempt to make an open source analogue to steamOS. And a pretty successful one, I'd say.

At least Valve leaves you root access when you buy their hardware. I don’t like Steam and normally use Lutris instead, which is certainly an option on Valve hardware as well.

The company and program aren't, the OS and hardware are, at least in the sense of user control.