Elon's rocket program isn't interfacing with anyone or anything. Here's the launch window, the permits are filed, and here's the orbit. Push the button and hope it goes. Operationally, there is very little coordination. That's great from an engineering perspective because he doesn't have to deal with all of the crap that exists outside of his bubble.
ATC will be a little different with birds, weather, runway closures, failed com's, emergencies, pop-up IFR, VFR, drones, kites, nuts in lawn chairs supported by balloons, Chinese balloons, non-ADSB helicopters, and a thousand other things I'm not gonna take time to list.