I mean when the hobby OS wants to shut down, it can power the machine it's running on down. Not unlike what would happen if you clicked power off on your desktop OS menu.
Getting it to work on GCP meant properly driving something called the Intel PIIX4 controller which was emulated into the VM.
Separately from the OS being able to turn itself off, the OS needs to process a signal received by the hypervisor on this controller to support the hypervisor gracefully shutting it down. Otherwise GCP will wait 90 seconds after it has sent the shut down signal to give up and terminate the VM itself.
The problem I was trying to solve was (a) OS can shut itself down in GCP (b) restarts in GCP from the GCP console would be instant, rather than take 90+ seconds