Try Steambot Chronicles! It's my favorite game of all time by a wide margin, but it's been forgotten by time. It's a really cool adventure game with a ton of different things to do, from piloting a giant robot to playing different musical instruments in a band, to decorating your own little apartment, and a bunch of other stuff! There's a lot of dialogue choices to make too that can affect how people treat you, and lead to a few different endings, including being a hero vs a villain. The graphics and soundtrack are great, too! I can't recommend it enough!

Gauntlet: Dark Legacy is great classic fun

Silent Hill 2

How is XIII via emulation? Would love to try that on my Steam Deck.

There are two amazing super hero games that I would recommend: Spider-Man 2 and Hulk: Ultimate destruction.

Spider-Man 2 was easily one of my favorite games of all time. This game essentially set the bar for what a Spider-Man game should be.

Hulk: Ultimate Destruction was an open world game where you were the Hulk and did all the Hulk things. I can't think of a recent game where you play as the green giant.

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.

Arc the lad 2 twilight of spirits is a cult classic

All the GTA games (GTA III, GTA VC, GTA SA, GTA LCS, GTA VCS). There are some good Need for Speed games too, and a bunch of great Tony Hawk games. TimeSplitters, SOCOM, and Red Faction are great too.

...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 >_<

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.

My entire childhood was Tony Hawk's Underground 2 on the PS2.

Ratchet and Clank games

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

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

Soul reaver

Grand teresmo

Rayman 2

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!

I absolutely loved KH1/2 FM

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.

Dance Dance Revolution!

Jak 3

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

Road Trip Adventure

I see Rule of Rose, I upvote.

Klonoa 2

Super Monkey Ball Deluxe

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

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.

Primal.