Thanks everyone for the replies, I've really appreciated them!

* How significant is the lack of some major third-party games on Nintendo?

Before it was very notable the platforms were more vehicles for first party game with some decent support, S2 however has turned things on its head with far more support than prior platforms to the point you may miss out on a few western releases were as before they'd mostly skip the platform and most if not all Japanese titles will be present also keep in mind some titles because of optimization can also release a bit later. A good way to test if the S2 support is ideal for you would be to watch the recent Nintendo Direct and the last few, NDs for the S2 are more focused on pushing the platform as a person's primary console so have way more third party titles, do this to gauge if the games you see are the type you go for and the amount is adequate.

* How noticeable are the hardware/performance limitations compared with PS5?

With S2 it's noticeable but not really game changing like before, the experience is very much comparable across all platforms now.

* Does Nintendo actually offer enough variety in terms of genres, or is it still fair to say that the platform is heavily focused on platformers and its traditional first-party franchises?

Tbh variety in their first party is unmatched they like to experiment a lot even with their major flagship title, one title in the same franchise even with the same core template can have a completely different experience to another. Nintendo's first party if very much about being open to give each game a look in to see if it's for you as they don't really aim for any one specific type of consumer.

* If I completely gave up PlayStation, would I end up missing a significant number of games that I would normally play on PS5?

Depends what you play on PS, if it's third parties you'll likely be fine with S2 as more and more support is finding it's way onto the platform. As someone with a high end PC I'm finding S2 to be very viable as a primary gaming platform.

* Given that I now have much less time to play, could Nintendo actually be a better fit for me than PlayStation?

In all honesty this is one area the S2's design shines better than anything else imo its concept is literally designed around someone customizing their gaming habits.

* Most importantly, can Switch 2 genuinely work as a complete, standalone platform, or is it still primarily a console that makes the most sense alongside a PS5/Xbox/PC?

Imo from what I've experienced from it and even as someone who also has a very good PC it can easily be a standalone console even more so if you're open to give things a try.

*Extra

One thing I'd give you the heads up on is I'd recommend getting a Micro SD card if you do decide to get one, I've been a digital consumer for a decade now so the whole GKC thing is not as much an issue for me but I understand it's not the same for everyone.

I've been a Nintendo only gamer forever.  I do have a PC, but I mostly play stuff there that isn't on consoles anyway like real time strategy games such as Rise of Nations and Command & Conquer.  Personally, I don't really feel like I am missing out, and a lot of the best AAA stuff has slowly been making it over to the Switch and Switch 2 if you are patient.  My backlog is a mile long anyway, so I am more patient than most.  I have always felt if you don't have a Nintendo console, you are missing out on some of the best games of the generation.  They really are that good as developers.

Action/Adventure
I am going to combine these two.  I feel like there is a lot of overlap here, so not going to bother with trying to split them.  I'm going to try and hit a wide variety of stuff in these lists.  Full disclosure, I have not played them all.  Trying to just grab popular and well reviewed games for the most part.  Plus some of my own bias is going to be in there. A lot of these games could maybe fall in multiple categories, but whatever.  This is first and third party combined.

• Zelda - The quintessential action adventure franchise in my opinion.  You have Breath of the Wild, Tears of the Kingdom, Link's Awakening, Skyward Sword, Echoes of Wisdom, the Ocarina of Time remaster coming, plus a bunch of older classic Zelda games if you buy the online membership.
• FromSoftware - Dark Souls, Elden Ring, the upcoming Duskbloods
• The Elder Scrolls - Oblivion and Skyrim
• Assassin's Creed - The Ezio Collection, The Rebel Collection, 3 Remastered, Shadows
• Fallout 4
• Onimusha: Way of the Sword
• Okami
• Bayonetta 1, 2, 3, and Origins
• Devil May Cry 1, 2, 3, and 5
• Astral Chain
• Pragmata
• SuperGiant games - Hades 1 and 2, Bastion, Transistor
• No More Heroes 1, 2, and 3
• Hyrule Warriors Definitive Edition, Age of Calamity, Age of Imprisonment
• Red Dead Redemption
• Luigi's Mansion 2 and 3
• Batman Arkham Asylum, Arkham City, Arkham Knight
• Alien Isolation
• Grand Theft Auto III, Vice City, San Andreas
• Indiana Jones and the Great Circle
• Outer Wilds
• The Outer Worlds
• Star Wars Outlaws
• No Man's Sky
• Hogwarts Legacy

RPGs
I feel like there are tons here, especially JRPGs, and I am probably going to miss a bunch.

• Xenoblade 1, 2, 3, and X
• The Witcher 3
• Dragon Quest 3, 1 and 2 HD-2D remakes, 7 Reimagined, 11, Builders 1 and 2
• Mario + Rabbids Kingdom Battle and Sparks of Hope
• Octopath Travler 1, 2, and 0
• Paper Mario The Thousand Year Door and Origami King
• Super Mario RPG
• Mario and Luigi Brothership
• Suikoden 1 and 2 Remaster
• Unicorn Overlord
• Final Fantasy Tactics
• Pretty much any Final Fantasy game you could want.  All the pixel remasters (1-6), plus 7, 8, 9, 10, 10-2, 12, the new remake of 7, the new one called Resonance (excludes 13, 15, and 16 which have not been ported)
• Pokemon Let's Go, Sword and Shield, Scarlet and Violet, Legends Arceus, Legends Z-A, Winds and Waves, FireRed and LeafGreen, Brilliant Diamond and Shining Pearl
• Fire Emblem Three Houses, Engage, Fortune's Weave
• Triangle Strategy
• Diablo 2 and 3
• Xcom 2
• NieR:Automata
• Star Wars Knights of the Old Republic 1 and 2
• Bravely Default 1 and 2
• Collection of Mana
• Front Mission 1, 2, and 3 remakes
• All the Kingdom Hearts games
• Live A Live
• Monster Hunter Rise, Wilds, Stories 1, 2, and 3
• Metaphor: ReFantazio
• Persona 3, 4, and 5

Platformers
Do I even need to list these games?  Nintendo excels here.  Plus there are a ton of indy games on the eshop that fit here as well.

• Super Mario Odyssey
• Super Mario 3D World + Bowser's Fury
• Super Mario Galaxy 1 and 2
• Super Mario Bros Wonder
• Super Mario Maker 2
• New Super Mario Bros U Deluxe
• Donkey Kong Bananza, Returns HD, Tropical Freeze
• Kirby and the Forgotten Land
• Ori and the Blind Forest, and the Will of the Wisps
• Braid
• Guacamelee 1 and 2
• Iconoclasts
• Inside
• Limbo
• Metroid Dread, upcoming Ravenous
• The Messenger
• Prince of Persia the Lost Crown
• Shantae series (there are 6 of these games)
• SteamWorld Dig 1 and 2
• Yoshi's Crafted World, The Mysterious Book
• Celeste
• Axiom Verge 1 and 2
• Bloodstained Ritual of the Night, Curse of the Moon 1 and 2
• Carrion
• Castlevania Advance Collection, and Dominus Collection
• de Blob 1 and 2
• Raymond Legends

Shooters
Maybe the weakest category for Nintendo consoles in general.  But not entirely absent either.

• Cyberpunk 2077
• Call of Duty: Modern Warfare 4
• Splatoon 2, 3, and Raiders
• BioShock 1, 2, and Infinite
• Borderlands 1, 2, and 3
• Doom (2016), Eternal, Classic 1 and 2, 3, 64
• Wolfenstein II The New Colossus, Youngblood
• Quake 1 and 2
• Turok 1, 2, and 3
• House of the Dead remake 1 and 2
• Crysis
• Star Wars Dark Forces, Battlefront Classic Collection
• Resident Evil Remake, 0, 2 remake, 3 remake, 4, 4 remake, 5, 6, 7, Village, Requiem, Revelations 1 and 2 (Yes, I lumped these all here. Sue me.)
• Metro redux, Last Night, 2033
• Metroid Prime Remastered, Prime 4 Beyond
• Star Fox

For me, just the Switch would be enough to play on.  I use a website called dekudeals to track game prices and my collection.   Looks like I currently own 70 Switch games, and have roughly another 150+ on my wish list to track prices.  Hard to tell the exact number because I also have hardware, gift cards, and duplicates due to special editions or collections so that some games appear more than once.  Suffice it to say, there is plenty to play as long as you have broad tastes.

Biggest absences for the Switch are probably Red Dead Redemption 2, GTA 6, Baldur's Gate 3, Star Wars Jedi Survivor, Clair Obscur: Expedition 33, Sekiro: Shadows Die Twice, the Battlefield games and probably a few others I can't think of right now.  Also some exclusives like The Last of Us or God of War or Spiderman or Halo that of course will never come to Nintendo consoles.  Some of those others maybe have a chance some day since the Switch 2 is quite a bit more powerful than the first one.

Moving forward, it is hard to say what developers will be targeting.  With graphics cards and RAM pricing as it is, I sort of doubt many developers will want to push super high end PC graphics.  That probably gives the Switch 2 a leg up to be a minimum target on the low graphics end for multi-platform game development for some time. Especially if it is successful like the first Switch.

Typical. Nintendo seems to be one of the few modern game companies that have any common sense left.