There has been alot of rumors about this..... the "strength" of its library would be native PS4 games playable on it.
And then if it sells well, probably gets 1st and 3rd party support ontop.

Such a device could probably do well enough.

price?
weight?
battery?

Even if the price, weight and battery are good, it does not compete with switch/switch 2. Nintendo's flagship games are too superior. And it also arrives 7 years late.

PSP was profitable but got clobbered by the mega-titan DS and even the aging Game Boy Advance was still competition before it was discontinued.
Vita was a failure, and pretty much DOA with the memory cards, price, and a shrinking handheld game console market.
A true PSP 3 (that is if you view PS Vita as PSP 2 which it pretty much is) is a big financial gamble for Sony. You have to build up a library of games between ports and native versions, an identity, proper pricing etc.
PlayStation Portal is a baffling product. Instead of that or a PSP 3, Sony should make a device similar to Steam Deck. PlayStation Now/Go/Remote or whatever you would call it with
1. Native PS4 library supported offline and online with or without streaming.
2. PS5 library supported when streamed from PS5
3. Bluetooth
4. Second screen functions with PS4 and PS5.

We're supposedly getting a tease of the Xbox handheld Sunday at the showcase. So... it begins?

I suspect the rumored PS product might be just a premium "Portal + PS4" thing instead of a dedicated handheld per se, though.

As a niche product like the Playstation Portal? Sure. If there's a market for that, then no reason why there's not an audience for something like this.

As something that's going to sell more than 30 millionish units? Probably not, and definitely not with the main selling point being the PS4 library. The PS4 is a generation and a half old at this point, and while there's definitely some people who would love to take their library on the go with them without having to stream, it's definitely not enough. It's unclear why indies would make that much of a difference, since those will for the most part play just fine on the Switch. They could make the shop a bit better, but it's not like the PSStore is currently amazing in that regard, and even if it were, I feel like the niche that would be interested in this are the type that could find the indie games they want just fine.

If it's going to be a separate platform from the PS5, then it would need to have strong exclusives. Sony was sort of able to do that with the PSP and failed to do it with the Vita. It's not clear why they would do any better nowadays. Even Nintendo, which had a strong history of supporting a separate console and handheld line realized that doing so wasn't really viable anymore. It's unclear why this would do any better than the Vita.

I don't get the love for the these handhelds and even worse one that is locked on playstation or xbox. get a 14 inch laptop that can play every nintendo game, ps2, and xbox everywhere, plus a massive selection of steam games.

And reopen manufacturing for that older hardware after they shut it down a couple years ago?

I don't see it. Not to mention that the APU wasn't designed for low wattage, so the device would have very poor battery life. 

You literally used the keyword (handheld), which is the appeal. Laptops aren't handheld, just portable. 

I was talking about myself. I don't get the love cause I can use a laptop and game everywhere just like a handheld but with a much better screen and controls, especially these bigger handhelds which are half the size of 14 inch laptop

How does a laptop have better controls?