@Strabysme @lynnesbian helpful hints from fox who used to play PS2 daily before irl made them stop playing games:
PS1 games on PS2 are a lot more fickle than regular PS2 games. Won't work properly even on 1080p TVs unless it's a Samsung panel IME. Idk why. Vizio, LG, and Insignia confirmed not to work.
PS2 on 4K is possible (upscaling required obvs). I've only ever used one 4K TV and it was Samsung as well, with a component connection. That worked ok.