Imho, the criteria is simple.

1. My personal criteria:

Does it play all major PS6 exclusives games while belonging to the PS6 generation ?

Yes. it's a PS6 device.

No. it's not a PS6.

Edit.: 

2. Objective criteria:

Playstation reports: if Sony calls the thing Playstation 6 and put sales together, the thing is a Playstation 6.

It's just like series S to Series X. You can argue that series S is weaker than Xone X, but you can't take away it's position as a "next gen Xbox Series X|S device".

Nintendo has a hybrid home console.

Xbox has 2 tiers of next gen home devices.

Rumor: Sony has 2 next gen Playstation devices, PS6 and PS6 portable. Both play the same games, both are Playstation 6.

What if the PS5 plays all the games that release on PS6 though. If PS5 is capable of running all PS6 games (which is will be if there's a portable), then it's hard to call it the PS6. This is why I don't think Sony's next console will be called PS6. I think it will called more like this. Playstation Portable. Playstation budget. Playstation Premium. 

You missed the part "...while belonging to the PS6 generation...".

The hardware needs to be 10th generation (PS6 generation). Otherwise, PS7 (if full backward compatible) would also be a PS6. lol

This just might happen if the price is actually as high as current market conditions suggest. No physical media will hurt sales, too. Releasing a console that is either way too expensive or less powerful than a PS5 (which a handheld PS6 or a "docked handheld" will be) is the definition of being stuck between a rock and a hard place. I hope prices will come down soon, but abandoning physical media was not a helpful move.

Playstation is probably comparable to Switch in China, certainly waaay closer to Switch than Switch is to PC. Did people already forget that "half if not more of the Japanese PS5's" were secretly going to China?! That's in addition to the official Chinese shipments lol.

And the Chinese economy decline is exaggerated. Not that I would expect PS6 to outperform the PS5 in China or anywhere else.

I think the video game market would need to CRASH for Ps to sell under 50 millions. I feel like people unfortunately forget easily and there isn't strong enough competition in Xbox to make the next playstation sink that low. It was pretty bad at the start of PS3, but they will use every way possible to sell their PS6 if it flops at first and a lot can happen in 8 years.

But i do think the video game industry is terribly positioned right now. There is issues that were there at the end of the PS4/One era that just have gotten so much worse that i doubt it will be resolved. There needs to be a humbling for some companies that have gotten way to comfortable. I'm just glad Nintendo kinda went all in with the Switch 2 even following their most successful era. The only thing you can truly come for them right now is the pricing for games (even though we don't talk about lowering the digital prices), game key cards (even tho it's third parties) and a soft line up so far.

I didn't miss that part. I just don't believe in generations being an arbitrary time limit that ends when a new console is launched. 

If the PS5 is MORE powerful than the PS6 handheld (which we are certain it is because the power saving mode is just a compatibility layer for PS6P) then it's not backwards compatible is it? Backwards compatible is when new hardware runs games from weaker older hardware. The PS5 will probably run all games even better than PS6P does. Doesn't fit the definition of backwards compatibility. 

I speak with all due respect...

Objectively, what you think and believe doesn't matter much.

Generations are defined by the industry and hardware manufacturers. If Sony and the industry define in the reports PS6/PS6 handheld as a single hardware family, then that is how it will be. They will put both hardwares together and count.

It's not about what I think though. If every new game releasing is releasing simultaneously on PS5/PS6P/PS6, it means they are performing together as one. You can call it a new generation all you want, but if every game released by third parties and Sony targets PS5 as it's primary platform it means we are just extending the old generation, not starting a new one  

The PS6P will be more powerful than PS5 for new games. It (unless downgraded) will have more RAM, more advanced technology, and much better ML and RT hardware. For unpatched existing games, it'll be weaker than PS5. For furure games, it may be notably better.

Also, "power" alone doesn't decide support. The Switch 1 was a lot weaker than PS4 and yet several games available on Switch and PS5 skipped the PS4. And if Sony mandates the handheld as a PS6, developers will be forced to either support it or skip it together with the home console. Microsoft and Sony didn't allow developers to support PS4 Pro, PS5 Pro, One X, and Series X without also supporting the base system. This is why not a single game exists that is crossgen with only PS4 Pro or One X