Despite owning a ps2 for like 5 years I've barely played anything on it...
My absolute favourite game on the system is Parappa The Rapper 2. I played that thing on repeat for literal months when I was younger.
Ape Escape 2 is great and definitely worth a look if you have PS Plus Premium!
Sonic Heroes and Sonic Riders are both great games despite Sonic Heroes being horrible on PS2 compared to GameCube, Xbox and PC