You cannot play PS2 games directly on any Xbox console—original, 360, One, or Series X|S. The hardware architectures are completely incompatible (PS2's Emotion Engine vs. Xbox's x86/PowerPC), there's no native emulation layer, and legal restrictions prevent unofficial emulators on the Xbox platform.
If you want the authentic experience with your physical collection, a Slim PS2 + component/HDMI setup is cheap and reliable. For convenience and upscaling, PCSX2 on a modern PC is unbeatable.