Also developed by a 3rd party.

Camelot, the only entry in the franchise made by them. But it's owned and published by Sony so just like Mario Golf (also developed by Camelot) it's first party.

The original post says Sony relied on 3rd party's for success, so I feel 3rd party developers also count.

Imagine it this way, let's say all of Nintendo's franchises aside from Mario Kart was made by 3rd party's and Mario Golf was made by Camelot wouldn't you agree in this case?

Agreed on falling quality from a lot of series that used to be big. Final Fantasy feels like the big one. On PS1 and still somewhat on PS2 Final Fantasy was THE role playing game series. Starting with FF2 (in the US) it was the premier RPG series, and also Square was by far the premier RPG maker through the SNES and PS1 days and still for the most part on the PS2. Now Square is just one of many good RPG makers and FF is just another RPG series. If you want RPGs now its not a choice of Sony or picking up scraps, and since Final Fantasy is no longer the series you HAVE TO buy if you love RPGs the case for buying Playstation gets a lot weaker.

Also there are so many good indie games, including RPGs, that come out on all the systems, really there is no requirement at all anymore to get Playstation if you are a jrpg lover.

And while some of the big Playstation exclusive games have lost their popularity, and also some of them have gone multiplat anyways, Nintendo has cultivated just about all the mega selling franchises in Japan.

The mega selling franchises in Japan now are:
Pokemon, Animal Crossing, Monster Hunter, Splatoon, Minecraft, and I think at this point we can say Mario Kart and Smash as well.
And the major selling franchises are:
Mario (2D, 3D, Party), Zelda thanks to BotW (guess we'll see if this continues or not in future Z games), FF, DQ, and Nintendo fitness (Wii Fit, Ring Fit)

Of those 7 mega selling series, 5 are Nintendo exclusive, one is on every device imaginable, and the other (MH) is now at least getting Nintendo versions of its series.
Of those 5 major selling series, 3 are Nintendo exclusive, one (FF) is still sort of PS exclusive but also finds its way to PC and Xbox sometimes and older games and side games in the series are often multiplat, while DQ should now also come to Nintendo consoles alongside PS and it will likely start to find a much larger audience on Nintendo in the future.

Basically, just about all the huge selling series in Japan are on Nintendo, the vast majority of them are exclusive to Nintendo. The big PS exclusives of old have either gotten less popular due to lowering quality and more competition and have also gone multiplat, while Nintendo has continued cultivating the series that the Japanese love.

How many other franchises back then were developed by Sony themselves? Sure if most of them were made by third parties then that is an overreliance on third parties.

It's worth mentioning that Sony owns Fate Grand Order, an absolutely massive mobile game, that has generated over 4B in USD mainly from Japan.

For a hybrid console like the Switch, you can't just look at the home console market, you need to consider the mobile market. But, if it is just limited to home consoles for this thread, then yeah, Nintendo dominates lol.

We're talking about Playstation here, not Sony as a whole. Fate/Grand Order is published by Aniplex which has nothing to do with SIE. They even publish games on Switch regularly.

Dragon Quest, after VIII, has been more on Nintendo’s consoles. IX was a DS exclusive, X was on multiple Nintendo consoles before eventually going on PS4 as well. Remakes of VII and VIII are 3DS exclusives. Even XI wasn’t a PS exclusive as it had a 3DS version and then a definitive edition that was a timed exclusive on Switch.

as for Final Fantasy, I’m interested in seeing whether or not Square Enix will be looking into the Switch successor? I know the modern FF games are primarily PS, but if the Switch successor is as powerful as rumored/leaked, is it possible to play FFVIIR or FFXV (or even XVI) at a reasonable performance? If the switch successor shows success and is powerful, it would be hard to ignore.