Tony Hawk’s Pro Skater 3 was pretty close to the peak of the series if you ask me, and the PS2 version was the superior one. THPS4 also came out on the Playstation 2. I see you already have Underground on there.

If you’d like something you can handily use to consume the rest of your entire life, Disgaea and/or its sequel will probably do you.

Ico and Shadow of the Colossus are also legendary. I haven’t tried in ages, I have no idea if modern emulators can get the latter to run at a non-crap frame rate. It’d be a lot nicer if so.

Odin Sphere is an often overlooked 2D action sidescrolling fighting thing wherein you Norse In The North and beat the shit out of absolutely everyone. Its sequel, Muramasa: The Demon Blade is much the same thing except therein you Ninja In The Night instead. The latter stayed locked to the Wii to my knowledge but the former was on the PS2.

The PS2’s library is quite vast. I’m not going to go looking this up to prove it right now, but I’m pretty sure it’s got the most titles ever released for a home video game console (i.e. not the PC) in history. Even just trying out unknown games at complete random, it’s likely to be able to keep you entertained in one way or another basically forever.