Games

Try out Shin Megami Tensei: Digital Devil Saga 1 and 2. It's one of those JRPG games with a lot of mysteries and loose threads and every single one of them end up solved by the end.

If you're a fan of the anime, the .Hack// games hold up pretty well. There's a little OVA that is included with each game to give more story.

Downhill Domination is... honestly stupid as all hell, but by design: it's a lot of fun :P

It's a downhill mountain bike racing game with a combat system, and it's ridiculous. You start being able to punch the bicyclists next to you; once you knock enough of them off their bikes you upgrade to being able to kick; then iirc you eventually get a stick or something lol. Otherwise, it's just another get-from-point-A-to-B-as-fast-as-possible game that doesn't require a lot of thought.

Just throwing out a fun game from my childhood, Lego Racers 2. I'll have to read through later for ideas because I'm in a similar boat in having never really been in console circles and never owned a PS2

...so grain of salt, cuz the name of this one doesn't sound right, but the screenshots look correct: Gradius V?

Side scroller arcade-y jet fighter - I remember it being good.

I just don't remember it being called Gradius >_<

Gauntlet: Dark Legacy is great classic fun

I absolutely loved KH1/2 FM

Soul reaver

Grand teresmo

Rayman 2

The Soul Reaver / Blood Omen games have not been recommended yet. Though, as a warning, last time I tried to do the Soul Reaver 2, there was a strange bug with the sound that made it so that you couldn't pass a certain puzzle.

Dark Cloud 2

How's PCSX2 performance on the Deck? I somehow get much better performance on my Ryzen 5 4500U laptop than I do on my Ally and that makes absolutely no fucking sense.

Ace Combat Zero! Or 4, 5, and Zero (in that order) if you want a lot of it.

Def Jam 2: Fight for NY. It's basically like some of the older WWF wresling games where there can be 4 fighters at a time, but you can only be targetting one at a time. But all the fighters are rappers. The finishing moves are awesome!

Crash Nitro Kart and some of the PS2 Crash platformers are pretty good. The Kart one has a boosting system that I like better than mario kart (and better items and vibes tbh)

Frequency & Amplitude:

The originators of the modern "rhythm game" genre.

Primal.

Not exactly a suggestion, but why emulate Okami instead of just running the PC version?

Edit: If you get the PC version, you should be able to use the touch screen to draw the brush techniques directly thanks to mouse support rather than having to fuck with the sticks. You also don't get the input lag from emulation.