It's not like the order's authority has to be constructed from constitutional primitives. So what? There is plenty in the order explaining it on the grounds of

It's not like the order's authority has to be constructed from constitutional primitives. So what? There is plenty in the order explaining it on the grounds of mitigating the spread of a deadly contagious disease within the states. The Health Department has a mandate from Congress to do exactly such things as that, and the CDC cites specific laws which (according to it) permit the order. It seems like you should be arguing that that law is unconstitutional, or unconstitutionally applied, or that the whole Health Department shouldn't exist or something... But instead you're saying that the order doesn't even claim to be authorized by law, which is false.