Yes, also Nintendo and Switch have a restricted library. That was and is said again and again. Switch is missing for instance realistic sports games and racers, cinematic story driven games and big shooters like Battlefield/COD. And I probably forget some stuff.

But claiming for Sony the most variety without any shading also shows blind spots. In the PS5 presentation I personally missed japanese styled games (as JRPGfan you should've noticed), anything turn-based or strategy games. Hopefully they will show more later. On the other hand - and that is the point I agree with the OP - with R&C, Sackboys Adventure and Kena they showed already increased interest in widening the library. I agree R&C is not a new series, but it was a long time between releases and I don't remember that much spotlight as it got in the presentation. Sackboys adventure goes beyond earlier releases of Little Big Planet. So clearly that are great signs for more diversity in the library. And that is a good thing for gamers.

To come back around (so that you don't see it as a jab at Sony): clearly Nintendo could push into more gaming demographics, if they would focus on some of the areas they currently neglect. But I assume every company has limited resources.

And as you did draw the comparison with Nintendo: I personally have difficulties deciding which console (PS4 or Switch) has a more diverse library regarding genres. Because genres are quite fluid and most people have blind spots for some genres, that others see. That is why you see very different declarations about the diversity of libraries based on what each one sees as a genre. For instance I see turn-based strategy and turn-based RPG as something different. Others may put all turn-based stuff into one genre or even outright ignore the different gameplay and group it with RPG and strategy. So a lack of turn-based games I might see as a limitation of diversity, while others point to non-turn based games as covering these genres. And I can't really say which view is 'correct'. They are all relevant. But that is why I don't think it is possible to really answer which platform has the most diverse library.

Well it is basically a strange comparison, Sony have more variety on PS4 than Switch even if we only considered third parties, the 4000+ games have all bases covered. There isn't any genre that Switch have games that PS4 wouldn't.

A fitness adventure game like RingFit Adventure, a sports RPG like Golf Story, a life simulation like Animal Crossing.

But probably you can nitpick and find something that has on a first glance the same genre. But this thread provides examples of the different direction, the genres I said are lacking on Switch: https://gamrconnect.vgchartz.com/post.php?id=9167930

Ask yourself if you see V Rally as a replacement for GT or Forza, Telltale as a stand-in for TLOU, Doom/Wolfenstein while good as approaching the same people as COD/Battlefield and the gimped FIFA on Switch being a replacement of the realistic sports games on PS4. And think if the games on PS4 you want to name are really having the same impact as the ones I named above.

Are we really inventing genres to fit?

Everybody Golf is a sport game with RPG elements if you want to go like that. The SIMS is a life simulation. fitness adventure?

For me it just seems like you are pretending there is a whole genre to cover a single game Nintendo created to pad the numbers.

I think sad dad is the wrong term to use. I think third person, action adventure with strong cinematic focus is a little more accurate. I do think people exaggerate this a bit, but Sony has definitely been focusing on games like this a lot more in recent years and I think that some people were a little afraid that they would continue focusing more and more on games like this and less on other types of games. The ps5 reveal seems to have put that fear to rest for some people because they showed a large variety of games and had little focus on these big cinematic games.