Most of the deck/dock screen issues are related to dock firmware and USBC display negotiation. The steam machine has built in HDMI and Display port which are presumably relatively bog standard.
The official steam deck dock seems to be fairly buggy, it's widely complained about. I've been using an Apple USB-C to HDMI adapter and it's worked perfect on every TV I've tried it on. Since the steam machines don't use USB-C video out this wouldn't be an issue.
That may be the case but “official valve hardware is buggy even after almost 4 years” is a troubling yet true statement when their entire pitch today was literally “check out our new hardware.”
I love my deck. But a smooth experience it is not. Up until idk a year ago…? Flipping from gaming mode to desktop mode or vice versa had a solid 50-50 shot of inducing a fail state requiring a hard reset.