Both a PS PC handheld and a PS portable console would "compete" against their PS home console.
The difference would be that a PS portable console would require resources to make its own ports and games, so it would reduce the current output of home console and PC ports. That wouldn't happen with a PS PC handheld because it would just run the PC games and emulate the PS classics. As a result, as happened in Vita, the portable console would get little support and catalog, while a PC handhelds have a giant catalog.
This only assumes SIE take one path (a suboptimal one) in terms of approach. If other rumors are correct, this handheld won't be a thing until around PS6's launch. If SIE have Mark Cerny and his team develop technologies which offload as much of the asset scaling and optimization tasks off developers as possible, the amount of money and resources needed to get PS games running on such a handheld reduces to a level far below the costs of developing PC ports of their games in the first place.
This also means whatever that technology is (advanced PSSR being one component) would be shared between the handheld and PS6; since the PS6 won't be running Windows or Steam OS, it'd be assumed the tech would be optimized for the PS6's OS. Therefore it makes the most sense for the PS handheld to utilize the same OS if it is using that same shared technology.
We are not talking about a PSP or Vita situation where a new PS handheld has its own library of titles; those days are over. But being able to natively play PS4 & PS5 games, downscaled PS6 games (using smart technologies that remove most of the work from developers) and legacy PS games is a much better choice than something that plays PC versions of PS games which would 1: run on an OS different from the PS6 and 2: leverage software out-of-ecosystem to propel its value proposition in a way that directly undercuts SIE's own PlayStation consoles through much less synergy.
These are the biggest reasons why a PS PC handheld makes little business sense; the only way it actually works is if the PS6 is also "basically" a PC running Windows or Steam OS. The next Xbox basically being a PC makes sense for Microsoft; it doesn't make sense for Sony/SIE.
I assume that before releasing that PS PC handheld they'd release their PSN PC storefront (which seems to be already in the works). I assume it would feature both 1st and 3rd party games, and that all of them would be crossbuy with their home console. So you buy a game once in PSN and if available you can play it both in PS home console and PC (desktop/laptop/handheld), because I think than to add this to the cloud cross-saves, cross-play, shared trophies, shared friendlist is the only way they have to compete seriously against Steam on PC.
There is no logical reason for SIE to rush for a PC storefront within the next 4-5 years unless they want to risk eroding value proposition for hardcore & core enthusiast early adopters to buy the next PlayStation console. Which will happen, as we saw similar occur with Xbox this generation. The only reason the collapse in Xbox console sales didn't happen sooner than it did this gen are because:
1: COVID/pandemic lockdowns/economic recession (ironically benefiting Series S)
2: PS5 & PS4 shortages during pandemic (greatly benefiting Series S, partially benefiting Series X)
3: MS 3P acquisitions of Zenimax & ABK (galvanizing the core Xbox fanbase, pumping some stock value into Xbox and keeping them in news cycles)
So, who are we expecting SIE to acquire in terms of major 3P publishers around PS6's launch? What pandemic are we expecting to see happen? Will the Switch 2 suffer from rampant shortages by the time PS6 is ready? Will PS5 stop being manufactured around then? Because any reality where there's a PC storefront prior to PS6's launch, just hurts the adoption rate of PS6 among a segment of would-be early adopters unless some
really big shit is happening around the brand or wider society to offset it and drive those hardware sales.
In specific to the PC PS storefront; without creative incentives there is little reason for 3P to prioritize putting their games on it when they already know storefronts like Steam will account for the vast majority of their PC sales. The probability of SIE doing on PC what Epic have been unable to do for several years, in a leapfrog way of only a year or two, is extremely low. And, it probably would come at the expense of some lack of focus on the console front, eroding things there further.
Preferably, there's no need for a PS PC storefront until nearing the end of the PS6 generation, which is close to or little over a decade from now. If anything, they should probably consider region-specific PC ports for markets like China via WeGame, if they feel that could complement console sales in such regions, particularly since console is still a very small market in places like China.
For their PC handheld they can do the same than for their home consoles: use PC hardware running on a FreeBSD Unix/Linux (case of Switch, PS3, PS4, PS5) but adding the Proton (also has BSD license and LGPL, Sony could use it for free) layer on top as SteamOS (which is open source Linux/Unix based, Sony can get what they want) to run the Windows games there as Steamdeck does.
And again this just creates far more value proposition for the PC handheld than their own console; you won't see SIE add Proton to PS5 or PS6 anytime soon for Steam OS or Windows emulation compatibility, for example.
A move like you suggest just drives down early adoption of PS consoles, and SIE losing a portion of high-ARPU hardcore/core enthusiasts to a platform where they will see less cuts from software revenue because of easy, open access to storefront alternatives.
And in that scenario I doubt they'd get enough mainstream & casual or new customers on console to make up the difference, especially if pricing patterns for console mirror what they have been this gen thus far.
