I'm not 100% sure what happened, and specifically why it happened now. It seems the supervisor process restarted and tried to restart all the processes in its /etc directory. I had a couple of old processes listed there, pointing to directories I had since deleted. Rather than just skip those, it errored out, bringing down the site. At least that's my theory. I deleted the old process descriptions and restarted the supervisor process.
I at least took the opportunity to apply the pending updates and reboot.