As much I’ve wanted one in the past, I don’t think I would be very much interested in an Xbox Handheld Gaming device today. It would have the same market problems that the Vita had. It would be pinched somewhere in between the Nintendo Switch, the smartphone that everyone is basically required to have today, iPads, and the Steam Deck.
An XBox Handheld would just be an also-ran, and launched in the muddled market of an older generation that insists on everything running on metal and a new generation that is less inclined to see the Cloud and mobile apps as problematic.

Such a product would have to be differentiated. What I would personally love to see is a dockable Microsoft Surface gaming handheld, as I don’t want to see the hardware outsourced to an ODM, that runs on an AArch64 chipset and is 5G enabled.
It could butt up against the Steam Deck price-point, offering full Windows functionality in docked mode and MSFT could throw in all sorts of software benefits to get people in the door, as well as a year or two of Game Pass.
Having a Microsoft Surface now after I endured the painful pre-iPad years of TabletPC has been wonderful. If this offered the same redemption of the UMPC form-factor, after having been a reviewer of those and owning several, and covered down on gaming as well, I’d be there day 1.

Of course, they could RDNA2 it à la the XBox Series chipset with some modifications, as others have suggested.
This, of course, is just about my dreams and desires as a techy. It says nothing about splitting Microsoft / XBox dev focus if they went down the route of differentiated hardware foundations and abstraction layers, the use of wrappers or something similar to Proton. It doesn’t consider the regionality plays and where such a device would do well and where in the world it might not. It does not talk about price point, how to stick the landing amongst gaming hardware but also within the Surface product lineup as well. Lots of issues would have to be considered.

But a techy can dream.