I remember Linux (and NetBSD) running on outrageously low-end hardware (even hardware without an MMU). While modern Linux is a no-go, would there any existing and relatively popular OS be viable?
If you're fine with obscure and retro, there's things like RISC-OS (ARM). Or EmuTOS (68k/ColdFire). Or FreeDOS etc (x86)
https://github.com/Mr-Bossman/pi-pico2-linux
That's with an 8MB external PSRAM though, fitting modern Linux in the internal SRAM is probably a step too far.