That's kind of their advantage. Their cloud service and home console use the same hardware, while their PC games use the same API and architecture. Presumably their handheld would do the same, being a handheld Series S in terms of capabilities and so being able to share the OS, games, patches, textures, everything. Their whole shtick is going where players are right now rather than waiting for them to come to their platform.
The thing for Microsoft though is that a handheld Series S would almost certainly come in UNDER NG Switch in memory and output resolutions, while a handheld Series X is impractical this decade. So it would have to undercut NG Switch in price, too. Can that be done with Series S specs this decade? Maybe.
Alternatively what we could see is next gen once again launching as a family of systems, with a handheld instead of a Series S, and a Series X equivalent super powerful home console, with a unified platform and CPU performance profile.
I think a handheld Xbox has real potential since they're very dedicated to the whole "unified ecosystem" thing. PlayStation I'm more apprehensive about, they don't have a lower spec device they can squeeze into a handheld, not even conceptually, so what would their device even be? What generation would it be in?