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!

You have to... No, You NEED to Play Downhill Domination. There is NO WAY you won't have fun playing that, trust me.
Oh! And Dragon Ball Z Budokai Tenkaichi 3! You don't have to be a DBZ fan to have fun with that, is amazing and so chaotic!
Also, have you consider trying Devil May Cry 3? (Don't worry about the number, it's a precule). It's kinda hard but so fun and satisfying.
I had the same problem too, but after trying to play them chronologically (and failing), I learned that you can play any FF game at any time, cuz they are very unique and don't actually relate one another.
Final Fantasy X is a great pick, for example, it helped me overcome my despise for Turn-base combat RPG.
And, if you're up to some Big Robot Fight mayhem anime style, Zone of The Enders is Amazing.
edit: AND YAKUZA! HOW COULD I FORGOT YAKUZA!!?? YOU HAVE TO PLAY THE FIRST YAKUZA ASAP!!
(unless you want to play / already played the kiwami version, which may be a better experience)