Very good question about authority to shut down businesses.
Im sure there is some emergency enabling legislation that lets politicos stomp all over our rights. (They love open-ended laws like that.) I assume the Supreme Court will have to decide if limits were exceeded or not.
Or we could launch CWII and hang them all. That would work too.
The U.S Supreme Court should have little to say on this matter. This is State government use of police power and their power over intrastate commerce. As far as our U.S. Constitution is concern, this is a 10th Amendment matter, it is between a States government, the State constitution, the States courts, and the people of the several states. As long as there is no unlawful discrimination in these orders, it is not the Federal governments business.