Since from Raspban's apt-repository, the many-machine-emulator MAME+MESS¹ works reasonalbe well on a Pi3 for many selected titles, and for more optimised emulation of popular consoles the Mednafen² emulator works even better, these two should also run extremely well on a Pi4 out of the Raspbian box.
Since these two emulators cover many retro machines, a handheld Pi4 is not so far away even with the standard Raspbian. No PS2 though.
(¹) Emulates most 8-bit and some 16-bit home-computers, several consoles, and most arcades.
(²) Emulates many popular consoles like Gameboy, NES, SNES, Megadrive, Saturn, Playstation.