It’s been driving me mad and I can’t find anything about it online.
macOS 13.1? appears to have solved this problem. Better late than never.
And even plugging in a charger before it actually died wouldn't save it: It'd try to turn stay on but the pending hibernation would kick in and it'd die.
The "fix" for me was to turn off deep sleep. Technically now they'll drain more during sleep, but that's preferrable than being broken during sleep.
The whole experience was disappointingly Linux though. Having to read through the Console to figure out it was a kernel panic and not a power issue, having to read through Darwin sources to track down where exactly in the hibernation it was failing, not the kind of stuff I expect to deal with from Apple hardware.
Oh, and the machine forgets its audio settings when this happens, too. Always tries to revert to built-in speakers while it's closed despite having a CalTech hub with speakers I've selected dozens of times.
I don't understand why laptops continue to have such weird power-management problems. I thought we fixed this stuff ages ago.