The Vita was a 3DS competitor, not a DS competitor. They kind of tried to outgimmick Nintendo with this one, unsuccessfully, I might add, because they didn't build the system around these features, but slapped them on in such a way that developers and players could just ignore them.
The PS5 controller is somewhat of a descendant of this device, although its features are a bit better supported - and it would be trivially easy to integrate them into a handheld.
As for processing power, they need to find a way to get the same CPU power as a base PS5 and enough GPU power for somewhere around 1080p (since going any lower would render many games designed for the home console unplayable) into a cost-, heat, space- and power-efficient package. Most of this work is on AMD, Sony just has to package it. Maybe they can get away with a system that simply forces a lower output resolution for existing games so that less GPU power is needed - or they wait long enough for it to be possible to miniaturize a full-fat PS5 into a portable device. I think the latter is unlikely though, at least within a time frame that would allow for a PS5P to coexist with the PS5 instead of the PS6.