You see, this is why I asked this question to begin with - so there can be more precise, concise information regarding PS2 aesthetics and how to achieve them. When looking for the answer myself, I mainly obtained statements similar to yours (With all due respect).
I understand that there are some similarities between the PS1 and PS2 even on a hardware level, but there were simply things that PS2 games didn’t do compared to PS1 titles, like the watery polygon jitter effect as a result of vertices being stored with less precise ints rather than expensive floats. Trying to work in how PS1 games achieved their look simply muddies the water.
As far as the art style is concerned, I saw prior posts that mentioned asking this question is vague when there were various cartoony and/or cel-shaded games that permeated the console.
This is why I purposefully excluded those, as a lot of their aesthetic styles comes from the specific visual design to begin with, rather than common PS2 visual development practices and limitations. I am asking how to make a game that looks, specifically, like the non-cartoony titles that effectively passed for “realistic”, such as Urban Reign, The Warriors, Rise to Honor, Devil May Cry, God Hand, Conflict: Desert Storm 2, Tony Hawk’s Underground, SOCOM US Navy Seals, Free Running, Yakuza, RoadKill, ATV Offroad Fury 2, 007: Everything or Nothing, NARC, and so on.
I’m not even mentioning games like The Red Star, TimeSplitters, Def Jam: Fight for NY, The Bouncer, or Second Sight due to their very specific, still exaggerated aesthetics being owed to their artstyle, nor titles like Fight Club or Metal Gear Solid 2 or 3, since their aesthetics were very specific and stemmed from particular shaders and filters that were far from commonplace compared to the other titles.
So with this criteria in mind, do you think you could please be more specific? Screenshots for the intended visuals added for extra clarity:
