The embedded people will naturally look at busybox. I saw it running on a credit card scanner at Old Navy a few years ago.

It has an init:

  $ /home/busybox-1.35 init --help
  BusyBox v1.35.0 (2022-01-17 19:57:02 CET) multi-call binary.

  Usage: init

  Init is the first process started during boot. It never exits.
  It (re)spawns children according to /etc/inittab.
  Signals:
  HUP: reload /etc/inittab
  TSTP: stop respawning until CONT
  QUIT: re-exec another init
  USR1/TERM/USR2/INT: run halt/reboot/poweroff/Ctrl-Alt-Del script

On an embedded system, that will be a strong contender for pid 1.