It requires a manual restart and it doesn't need to cool off. The power draw seems minimal compared to what driving it would be. When it's powering the home, the truck makes little to no noise.
I have the same setup (generator inlet box and interlock switch) and live in the Seattle area. We just went through 5 days without power and the Cybertruck powered everything wonderfully. Even had enough power to run the washer and dryer. Given how it performed, I wouldn't recommend the Tesla...