There’s usually two parallel processes going on during a black-start: spinning the power plants back up to get them synchronized to the grid, and getting power back out to all the consumers. Power plants have breakers that disconnect them from consumers which they keep disconnected until independent connections to other power plants allow them to spin up their massive turbines and synchronize them to the grid. There’s also tons of other downstream breakers at substations which will be in various states of functionality.

The power plants with direct connections have hard lines and black-start procedures that get power out to the most important customers like telecom infrastructure, which provides the rest of the comms. In a real world full restart it’s going to mean organizing workers at many substations to babysit old infrastructure so cellular is pretty much mandatory.