Just start with Wikipedia, OK? "Powers available under this Act are limited to the 136 emergency powers Congress has defined by law...."
https://en.wikipedia.org/wiki/National_Emergencies_Act#Emergency_powers https://twitter.com/Mivo68/status/1250134769175801864

These "range from suspending all laws regulating chemical and biological weapons, including the ban on human testing...; to suspending any Clean Air Act implementation plan or excess emissions penalty upon petition of a state governor;...

"to authorizing & constructing military construction projects...using any existing defense appropriations for such military constructions...; to drafting any retired Coast Guard officers... or enlisted members...into active duty regardless of ineligibility for Selective Service."

These all authorize the use of federal statutory powers. None of these powers authorize commandeering state governments. And I would need to see what particular power is supposed to trump the state police power under the Supremacy Clause.