An Xbox branded ROG Ally isn't going to make any difference one way or another in that regard.

For a modern handheld device, Switch 2 will be the first natural point of comparison in consumer's minds. The key selling point for this machine will be the ability to take your Xbox games with you, but that limits its primary appeal to the diminishing pool of people who still care about Xbox.

One of Microsoft's conditions seem to be confusing names.

ROG Ally / ROG Xbox Ally / ROG Ally X / ROG Xbox Ally X.

At least they could have named the announced "ROG Xbox Ally" the "ROG Xbox Ally S"... both to differentiate it from the first "ROG Ally" and to keep the low tier / high tier classes S + X similar to "Xbox One S / X" and "Xbox Series S / X".

This is about OS, not about actual piece of hardware - you have plenty of PC handhelds who are already quite a bit more powerful than SW2, but that is completely irrelevant.

Valve already pretty much won digital game marketplace war, MS can't risk letting SteamOS becoming default OS for gaming, and Valve is on the offense, so to speak, with "Powered by SteamOS" initiative.

An Xbox branded ROG Ally isn't going to have any impact on any of that; PC handhelds are a tiny niche market and Xbox is a dwindling brand.

And as I already said initially, it's a first step - if this gaming improved Win11 works as advertised, this will give manufacturers much more technically appealing option than SteamOS, since, if their handheld is not loosing performance on regular Win11 (which it currently does), only other appealing thing about Steam OS is that it's (presumably) free.

SteamOS is invading other devices... And it's focus is pure gaming.
Microsoft is trying to halt that advancement by engineering a fork of Windows 11 that can halt that advancement by SteamOS.

It's not about the hardware, it's not about Nintendo, it's not about Sony.
It's about the OS, one of Microsoft's biggest cash cows... Microsoft is partnering up with Asus to be the launch-pad for a gaming optimized fork of Windows that can be used by everyone.

This is more than just Xbox games, this enables you to play all PC games, even from Steam. This is about keeping Windows relevant.

This is a war over Operating Systems.

This.

And the handhelds are likely a launch pad, Microsoft doesn't want even a few million hardcore gamers talking about how much Windows sucks for gaming and how much better SteamOS is because SteamOS will expand to other devices, then eventually talk about how much better it is for handhelds becomes talk about how much better it is for PC.

It'll start with Handhelds then Tablets then Desktop PCs.

A large chunk of the reveal was Xbox talking about the Windows gaming improvements, they've also confirmed the Xbox UI/UX is coming to other devices soon, the stripped back Windows/Xbox UI/UX was a heavy featured selling point from them. They are trying to stop SteamOS before it grows into a big problem for Windows. Microsoft doesn't care about competing with PlayStation or Switch anymore, Windows is far more important to them and PC market is the biggest gaming market.

Microsoft and Steam are about to enter an OS battle and we'll see a Gaming focused Windows and SteamOS being spread to multiple devices. Eventually it will very likely reach PCs themselves, with a stripped back Gaming focused Windows OS which has an Xbox UI/UX. That will likely be their Series X successor which sounds like it will be some Xbox/PC hybrid device.

Doesn't matter if they don't sell gangbusters, that's not how the PC market works, it's about expanding the ecosystem and having multiple routes of entry into it. Increasing engagement. It is why they still make things like Surface. If the Xbox themed handhelds only sell a few million, and the Series X/S successor only sells a dozen or so million, I don't think they'll care, because it's all one arm of a massive PC ecosystem and for Microsoft that is about expanding Windows and maintaining their dominance, drowning out any competition. SteamDeck is likely a success for Valve and they're going to use it to become a bigger problem for Windows.

If SteamOS takes off then Microsoft will have a much bigger problem than the console wars, Lol. They need to try to extinguish the fire before it burns the forest down. We're talking like, at least 600m-800m+ PC Gamers and the majority of them game on Windows, if Microsoft doesn't act now then SteamOS will only grow and take a massive chunk of Windows users from Microsoft.

I get that their intent is to fight Steam, but the hardware itself is still going to be competing with other handheld devices for consumer's money and mindshare.

The hardware is just a clone of the Rog Ally with some Xbox branding and features. 
It's a Rog Ally.

It's all in the software.

And as a ROG Ally it competes with Switch 2, Steam Deck, Aya Neo, MSI Claw, Legion Go, etc for consumer's time and money.