Shining Force NEO and Shining Force EXA are both great underrated action RPGs.

Id look up the GT4 spec II mod. it adds a bunch of features to the game and even the Valencia track from Tourist Trophy

Klonoa 2

Super Monkey Ball Deluxe

Beatmania IIDX (if you don't mind connecting a keyboard to play)

I see Rule of Rose, I upvote.

Road Trip Adventure

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.

Frequency & Amplitude:

The originators of the modern "rhythm game" genre.

Ratchet and Clank 3 is missing.

Fatal Frame II

Mister Mosquito

Gitaroo Man

It's a little cringe in retrospect, but I really liked my time with Makai Kingdom. Avoid if anime stuff isn't your bag.

Ico had some interesting ideas that are worth a look.

Rogue Galaxy was pretty okay.

Psychonauts deserves a mention, though it's kind of obvious.

Red Faction had cool political leanings for a game of that era.

You've got heaps of great suggestions already so I'll leave it at that.

Definitely play the AC games. Which series am I talking about? Both.

Armored Core and Ace Combat are really good games. For the PS2 continuity of Armored Core it is arguable that the PSP versions are better due to the extra content, but otherwise it's not too big of a deal.

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)

Ps2 Mortal Kombat games were the best, they have beem sliding ever since.

Deadly Alliance is a slog for story/Konquest but a fun game.

Deception is so so good, one of my favourite games ever. Doesnt really hold up as well as Id like but it has brilliant features that I miss in every modern iteration. Namely the best konquest implementation. Chess Kombat.

Shaolin Monks, another one on par with Deception. I have to replay this next.

Armageddon is carnage, just fun fun all the way through. Every character from the entire run of the franchise is playable, it is everythimg.

Primal.

Monster Rancher 3. The monster rancher games were favourites of mine as a kid.

GOD HAND- the granddaddy of Platinum Games's combo based "beat em ups", made by Clover Studios before they went bankrupt and reopened as Platinum. So think Devil May Cry and Bayonetta but hand to hand 🎵"or fist to fist. Kick your nuts or twist your wrist. God power keeps my pimp hand strong so trust me or you won't last very long."🎵 Yeah, it also has quite possibly the best theme song ever too.

Zone of the Enders the Second Runner drops you into the midpoint of a fairly generic mecha anime plot, but as overseen by Hideo Kojima. It has a lot of "Dynasty Warriors" style "tear through hundreds of fodder with ease" gameplay, but also a very fast paced "attack/dodge/parry" system for fights against beefier enemies that ends up as this fast paced sort of rock paper scissors as you have to adapt to use the right technique to counter the enemy. You fly and can manuever very fast, attacks can come from any angle, and it's just flat out fun to control. There is a PC port/remaster of questionable quality (and no steam deck support), and a xbox 360 port of good quality, but it's mostly just uprezzed graphics that you'll get by emulation anyway.