If you're interested in games that work really well on the Pi without config, try out Sonic Robo Blast 2 on Flathub. But back to if you just want to play PS2 games, and do nothing else with the Pi, possibly you could look into Mini-PCs? They're low-cost like the Pi, but run on normal x86 CPUs, so running PS2 (or even PS3) games would be easier on there, if you're just planning on using a Pi for playing PS2 games.

Maybe you just stick with the defaults? I've gotten PSP games running at 120 fps and 4K on the Pi4 (although it still appears 60 because my screen is only 60hz). Is it just me or do you just think the Pi can't run emulators/games very well? I got Dolphin running really well with minimal overclocking, but lots of configuration. The best you can expect to emulate well/good/okay is the PS1, Dreamcast, and PSP, only because there's very good ARM codegens for PCSX-Rearmed/Duckstation/Flycast/Redream/PPSSPP. What you'd need is an emulator that's actually written for ARM64 *and* Vulkan, and even then i'm still not optimistic on the results. Win11ing either will not produce miracles for a small Broadcom ARM SBC. PCSX2's too firm in x86 optimization that it's still trying to go x86_64 and is currently in the process of reworking itself of old plugin system cruft. Play!'s barely usable on today's x86 desktops.

Install ps2 emulator