PS2 and/or PS3 emulation

I am interested in a very narrow gaming experience. I want to play all Pokemon that I can as well as sly cooper on the PS2 (and PS3 remastered if possible).

I hear that the AYN Thor can emulate pretty much all of the Pokemon games up to the switch (I have a switch, so no need to go that high anyway. ) Is it powerful enough to emulate PS2? What about PS3?

Also any other recommendations? What is the best overall and potentially best budget handheld to fit my needs? I’d like some options to choose from.