While FH4 isn't on Switch, Grid Autosport (which runs on the same engine as the mobile version of FH4) is available and offers realistic handling on a portable device.
Forza Horizon 4 is a modern Xbox/PC title and cannot run natively on PPSSPP (a PSP emulator). Attempts to play it via PPSSPP are not possible because the game’s platform, system requirements, and architecture are incompatible with the PSP hardware emulator. However, there are alternative ways to get a similar or satisfying open-world driving experience on lower-end hardware or via emulation of other platforms — and some community projects and ports that may interest fans.
Since PPSSPP is a dead end, here are legitimate ways to play Forza Horizon 4 on the go:
These handheld PCs run Windows. You can install the Xbox app or Steam and play Forza Horizon 4 natively at 60 FPS on Medium/High settings. This is the "PPSSPP dream" fulfilled by 2024 hardware.