The Switch literally has all of the advantages you mentioned.

"As it was declining in the major markets, a lot of new markets were opening it."
The Switch is doing a lot better in RoW than any previous Nintendo console.  It is reaching new markets.

"It also was so dominant during its gen that developers kept supporting it for quite a while after its launch."
Third party support keeps increasing for the Switch.  Third party support for Switch in 2021 will be far better than every year before it, and 2022 will likely be better than that.  That is because 1) handheld developers are taking a long time and 2) home developers took a couple of years to take the Switch seriously.  On the handheld side we are just now getting successors to several 3DS titles (Monster Hunter, Bravely Default, Rune Factory, ect...), because Switch is a lot more powerful than 3DS.  These handheld developers are adjusting to the big bump in power.  Home console developers didn't want to back another Wii U, but it's very obvious at this point that Switch is going to have a huge install base.  New games usually take about 3-4 years to develop.  Up until now Switch mostly got ports, but we are actually getting to the point where Switch is getting its first wave of original 3rd party games.  Expect later waves to be even bigger than the first wave, because that is how it is on every successful console.

"Also, Sony wanted to keep pushing the PS2 after the PS3 was released"
Nintendo supported the 3DS for two years after the Switch released.  If they will do that for a system that sold about 76m, then how much longer will they support a system that will sell about twice that amount (or more)?

On top of that Switch has even more advantages over the PS2:
-Switch is currently tracking ahead of the PS2.
-Switch has still not had a price cut.  PS2 had several price cuts by this point.
-Switch is selling to both home and handheld markets.
-Nintendo are pros at selling multiple handheld systems to the same household.
-Switch has several evergreens that have already outsold the top selling PS2 game and will likely get more.

And, Nintendo has a history of not supporting their systems very well as a new one is coming out. They didn't do much for the Wii after Skyward Sword. Aside from Pokemon, they cut support from the 3DS pretty quickly as well, despite it being a massive success. Unless they change course, I wouldn't expect to see the Switch being pushed hard.

Switch is tracking ahead, but I'm pretty sure that the same could have been said for the PS4. The PS2 sold about 1/3 of its units after the PS3 came out, and that kind of thing hasn't been seen since. The Switch would probably need about 120-130 million or so before a successor is released to have a chance. It's possible, but iffy.

Yeah, but if the Switch Pro is DLSS with a 4K screen, this won't be like the DS to DSL or 3DS to New 3DS.  This will be like a new console generation and Nintendo is going to want to push people to the newer model since the games getting released for the Switch Pro (e.g. BotW2) are going to look really ugly on the old Switch assuming that there even will be backwards compatibility.  Maybe the rumors are wrong and the new Switch is not a major hardware upgrade, in which case I will say that you are right.  But if the hardware is being overhauled the way that we are hearing, then Nintendo is going to want to push people to the new platform.