Are gamers expected to rebuy their PS5 library for the HH or is it shared with PS5?

If it's shared, how does Sony make a profit on the HH?

This is my only concern. If I can share a library I would buy it no thinking needed even at the cost of DRM. But im not willing to rebuy games for it.

But that dosent mean sony would not make money. Would probably mean that people buy more games. As there are games that would be better suited for handheld and for consoles wich you would probably be incline to buy just one if you had either the handheld or console. Like for me theres no way I would play a turn base rpg on my ps5 but I love to do so on my switch. And the same as I dont play data pace action games on my switch but do on ps5.

Also there will be plenty of people who only choose one form factor. But yea. I see this just like the steam deck. It would mostly attract people with an existing ps5. 

Sony has to support its own products before fans will jump on board.  While the vita was a nice pice of hardware, there wasn’t any software on it worth having.   It was just a jumble of ports and niche games.

I think there are too many problems with a "shared ps5 library" approach and it comes heavily down to developer incentives. What Valve is doing with the Steam Deck is giving people the ability to play PC games on the go but they aren't guaranteeing that every game will be playable or meet a certain standard. They aren't going out there and being like, if your game doesn't work on the Steam Deck, we won't let you sell on Steam. They are simply giving a device that can play modern PC games on the go but no developer is going to be forced to scale their games down for it. So if a developer makes a PC game too demanding for it, Steam Deck users will simply have to skip it or play it on a more powerful PC. Heck, Call of Duty can't even fit in 2/3 models. The main draw of the Steam Deck is that it's a portable PC that can play games.

Sony can't do that with a "shared ps5 library". For that to work, Sony would need to force developers including their own to scale their games down to base PS4 levels. And I really don't think that's going to work cause either you will need to re buy all your games as those devs will need to be making special versions for it or if you don't have to rebuy them like with Steam Deck, then the publishers will be pissed that Sony is going to make them do all this work for free. We have seen devs complain about 4TF on the Series S. Now imagine 2TF with even more limitations.

That's an excellent point. Nintendo is the only one of the big three that almost never takes losses on hardware sales. Sony and Microsoft make the vast majority of their video game profits on software and subscriptions. A portable refresh of the PS5 (with weaker specs but still able to run the same library) would run into a huge problem there. If it just has PS5 software, why put in the R&D plus everything else when you can just sell the same games on PS5?

Double the Ram capacity, significantly better CPU and a far more efficient GPU isn't just "a bit better than a PS4".

The only thing that could potentially hold it back is fillrate due to limited DRAM bandwidth. (DDR5 @80GB/s~ probably not doing it any favours.)
But with draw stream binning rasterization, primitive shaders, delta colour compression... It should be close enough to be irrelevant.

Add in a spinkling of Ray Tracing, far better geometry performance, smart access memory, potentially an infinity cache, Fidelity FX/Super Resolution, Rapid Packed Math... And the list of hardware improvements over the Playstation 4 is rather extensive on the GPU front.

While true, "for free" is asking a lot from publishers. Resolution is just one aspect of the game. You can see this with Witcher 3 Switch vs PC comparison.

While specialized versions are doable... "For Free" is not unless you want them to re-buy those games.

The Valve announcement has people looking at a portable that revolves around the steam store so doesn't have many of the issues that would face a console based portable and the first thing that crops up is wanting a PSP5 followed straight up with arguments over a jumble of tech specs/ pricing etc, instead of more importantly following Rol's lead and firstly looking at goals and ROI concerns and viability issues . Human nature or something else?

More entry points into the PS ecosystem (think of Japan for example), higher engagement due to more ways to play & launching at a break-even price (selling for profit for most of its life).

Worth remembering that part of this handheld revolution we're seeing is due to the acceptance that handhelds do not need to fit in the pocket to be appealing. Mobile chips are also scaling at a faster rate than desktops. All of this makes powerful handhelds more financially viable than they were before.

But I agree there isn't some obvious jackpot for Sony to hit even if it succeeded, which throws doubt on whether its worth taking the risk

Safe to say OP wants PS to re-enter the mobile gaming space.