PS3 graphics aren't that different from modern day graphics, just lower fidelity and the hardware was a bit quirky but other than that they didn't have any particular aesthetic; I don't think the PS2 had either. The PS1 did though, the weird texture shimmering that was reproduced in for example the Bloodborne demake [0] and subsequent Bloodborne Kart, which had to be rebranded to Nightmare Kart for copyright reasons. But that one's made in Unreal Engine 4, with a forum thread [1] saying the effect can be reproduced across multiple engines like UE4, Unity and Godot, using a shader.

[0] https://b0tster.itch.io/bbpsx

[1] https://itch.io/t/1999076/what-game-engine-did-you-use