It's currently handled by running many independent regions so that data centers can be brought up from fully dark by bootstrapping them from existing infra. I haven't heard of anyone bringing the stack up from a full power-off situation. Even when Facebook completely broke its production network a couple years ago the machines stayed on and running and had some internal connectivity.
This matters to everyone because while cloud resources are great at automatic restarts and fault recovery there's no guarantee that AWS, GCP, and friends would come back up after, e.g., a massive solar storm that knocks out the grid worldwide for long enough to run the generators down.
My guess is that there are some dedicated small DCs with exceptional backup power and the ability to be fully isolated from grid surges (flywheel transformers or similar).