The PS2 came out in that magical era in the early 2000s where games were taken seriously enough to get proper AAA funding and development, but the industry was still young enough that developers were not quite set in their ways and simply recreating the same standard forgettable experiences over and over again and grubbing as much money as possible.
Back on topic though, PS2 action games wise: "Extermination" is interesting. Third person action, though no super powers. It's more Resident Evil with space bug aliens.Nothing else springs to mind immediately.
"Extermination"
"So many good games on the system"