I got through phases of games, and right now I'm in the one I like to think of everything-modern-is-making-me-angry-so-I'll-turn-back-to-vintage-games - and that's in the form of PCSX2 on my Steam Deck.
Playing the PS2 generation on the Steam Deck is kinda the 'perfect' generation: I can upscale the resolution without a performance hit, I can apply HD texture packs, Retro Achievements and I can drop the TDP to extend the battery life.
Anyway, I never had a PS2 (it was just a touch before my time), so there's so many games I'm yet to discover there. I'd love to hear any suggestions you might have for what I can play on there:
Just a couple notes:
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No GTA games because they're better with the PC versions. While I've bought the games, the account that Rockstar demands people have to play their games makes me angry on principle (a single-player game forcing an online check each week to be able to play it? No thanks), so I've got cracked versions to play.
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No Final Fantasy because I'm not even sure where to start!
So if anyone was around back in the PS2 era, and has some recommendations for games they've loved, I'm all ears. I've been having such a fun time playing these.
Some big thanks to my friends who made and run RetroDECK (my choice for emulating on the Steam Deck), and to the PCSX2 team (who I'm chatting to right now actually, so keep an eye out and in a week or so I'll share that chat with them all about creating and maintaining the PS2 emulator!)
Also, if you do have a Steam Deck, and want to play with the HD texture packs I do, then it's really simple. Just download the pack, and name then according to their game's I.D. code - SLUS-20743 for example, then place it in the texture_packs folder:
From there, go into PCSX2, then right-click the game, select properties, graphics, texture replacement and tick the two boxes I have:
Then you've got the games looking the best they can be!
Here's a link to a stack of pre-done HD textures for a lot of PS2 games, to help you on your way!

I see you've got 007: Nightfire in that list, so let me raise you 007: Agent Under Fire. The single player is not as good as Nightfire, but the multiplayer is spectacular, as it lets you turn on fun modifiers like moon gravity and use gadgets like the Q Claw on any surface instead of just preset spots. They probably toned down the multiplayer in Nightfire because Agent Under Fire's didn't feel very Bond-esque, but Bond or not, it was a ton of fun. The multiplayer is up to 4 players split-screen on Gamecube, but I can't tell if it still retains that on PS2; often times, back then, PS2 games only had 2 player support while Gamecube and Xbox had 4. This was because the PS2 was weaker and also required an extra peripheral called a Multi Tap to hook up more than 2 controllers. Find some friends and play some deathmatch, if you find yourself in a situation where you can dock your Steam Deck or otherwise play on another computer.
There's also Metal Arms: Glitch in the System, a third person shooter where you play a robot who can take over other robots. It's quite challenging, it's got a sense of humor, and it's probably one of the best games of that era to not get remastered in a modern port. Once again, we've got the multiplayer issue rearing its head, but I'd strongly recommend the single player for this one, too. I also played this on Gamecube back in the day, so just play whichever version is rated best for compatibility in your emulator of choice.
You might also want a Burnout game in your library. Most people seem to prefer Burnout 3: Takedown, but my Burnout of choice was Burnout Revenge. Both great. I wish we got more racing games like these today. Local multiplayer is a dying breed in this genre.
You've got Tony Hawk's Underground in that list, but for my money, the best game in the series is Tony Hawk's Pro Skater 3.
The first three Ratchet & Clank games on PS2 have not been topped by their later entries, as far as I'm concerned. Ever since the fourth game, Deadlocked, the best they've been able to do was to remix ideas they've already used.