I see no evidence for this, and plenty of evidence to the contrary. Notably, after the initially failed Steam Machines, we now have Steam Deck, Steam Machine Mark II, Steam Frame, Steam Controller Mark II, etc.
And critically, Valve seems to be learning, iterating, and the Steam Deck and Steam Controller Mark II are both much more enjoyable to use than the first Steam Controller.
From their perspective, Valve are otherwise dependent on Microsoft or Apple who see them as competition to squeeze out. Success of the Steam hardware platforms is their only way to change that situation. Therefore all evidence points to Valve continuing to iterate until they find success. They are a private company, so they can afford to do so indefinitely without worrying about pissing off a board or investors.
Eh... again, Valve being a private company plays a role here. Whoever succeeds Gabe will likely be chosen by Gabe, not some board or activist investor looking to maximize short term profit. There is much more freedom in private orgs to make long term strategic decisions.
The 10 years Valve took between Steam machines was invested (wisely, I think) in Linux infrastructure like Wayland, Wine/Proton, GPU and audio drivers, etc. None of which Valve will have to repeat.
To make my point, there was only 1.5 years between the release of the Steam Deck, and Steam Deck OLED, and that involved a new silicon tapeout.
I think it all depends on what their mission is, what bits of the larger ecosystem does valve care about or not care about, what do they want to defend or destroy. I'm tempted to say "defending the store is existential for them" but the scale of it likely gives them an extremely big comfort zone. Whatever OS the users have isn't going to affect whether they can do commerce through them unless MS does something unhinged like getting rid of win32, or as the fear around win8 that they'd centralize all windows software through their channels.
If their mission is SteamOS, then I'm tempted to say they need to expand their area of influence beyond what they're doing with linux now which seems to be strictly game related, which likely involves whittling down the major or minor reasons people don't use desktop linux (and all the projects that comprise it) in general, not just their distro. So long as they're supporting (in one way or another) the majority of windows games in a foreign environment and the richness that mods can bring they could do with improving the experience of that relative to windows and not just the happy path of what happens if the base game launches. And that's before the enigma of anti-cheat. Then find some way to reap the rewards, if any, for doing that greatly expanded workload or investment.
Steam has already failed at this once, and it won’t try a third time.
(And Windows is currently at its lowest point, so it’s the perfect opportunity.)