The PSP's CPU was basically a PS1 CPU with 10 times the clock speed. Emulating the rest of the PS1 system isn't hard from this starting point. In contrast, full system emulation, the kind required to get PS1-3 games on the PS5, is quite rare as a way to implement backwards compatibility.

BC is usually implemented by being hardware-compatible from the start (GC->Wii, PS4->PS5) or including at least part of the previous console's chipset if not the whole thing as auxiliary processors.

Also you're ignoring that good N64 emulation with high compatibility and accuracy is still very much a work in progress. The first N64 emulators were incapable of playing most games on a fundamental level.