For me it was encapsulated by doom 3 for the most part. Games with strong dynamic shadows like splinter cell chaos theory and stalker with a mix of shiny specular effects is timeless for me. When I go back to these games the shadows still feel as good as they did when they came out and the lighting perfectly crafting the mood. A lot of modern games now even though their fidelity on paper is much better just always feel extremely flat to me and don't pop out of the screen like they used to. It seems like they're missing contrast and UE5 seems to make this even worse where all the games using it just look like mush
The difference between a PS1 game to a PS2 game was huge. I think the last real PS2 games that were released between 2006 - 2008 felt like they were really pushing the PS2 to it's limits, except for the weird PSP and Wii games that were ported for the PS2, those had bad graphics.
Yeah it was really exciting seeing what developers were cooking up plus it was a time when art direction was huge and you had really talented people making these games look visually interesting.
Can't forget about MGS when talking about pushing the PS2 to its limits. Both of those games look absolutely amazing. Both quite stylized while having some of the most realistic graphics of the console
Gran Turismo 4 and the Silent Hill games (except the PSP/Wii version) were also very good. I think there were a few other fighting games and RPGs with very good graphics. And speaking of PSP, Parasite Eve 3: The 3rd Birthday looked just like a PS3 game on PSP, which is impressive.