Get a Raspberry Pi 5 or a mini PC instead of a stick, or something FPGA-based like a MiSTer if you don’t mind spending some money.
Pi 5 isn’t too expensive. Raspberry Pi 4 was already pretty good for emulation, and the Pi 5 is noticeably faster than the Pi 4.
Firestick is way too underpowered to emulate PS2 games. At best you’re going to get N64 and PS1 with inconsistent frame rates. It’d work fine with NES, SNES, Sega Genesis etc though.