edit:

To expand on this, for an individual's right to do something to be protected from the states that right must be protected under the 14th amendment. Over the years the court has found that the 1st, 2nd, 4th, etc, basically all the big stuff is protected from state infringement under the 14th. In addition to this, for the incorporation of a right to under the 14th to have any teeth to this the court must have ruled that state regulation must pass strict scrutiny to be constitutional, in layman's terms it needs to be limited in scope to the bare minimum and there as to be a damn good reason. Unless you're willing to play some serious mental gymnastics there isn't any real combination of constitutionally protected rights and court rulings that restrict infringement on those rights that result in the ability to run a nail salon or other "clearly not essential" type business. Basically, no the constitution doesn't protect you from this.

That's where civil liberties advocates old nemesis comes in. In Wickard v. Filburn the court ruled that even non-business activity that is fully contained within a state is subject to federal regulation under the interstate commerce clause because it affects market conditions if everyone does it. If this sounds like an end run around the constitution it's because it is. Normally you see this ruling used (I'd love to say "abused" but is it really abuse when it's functioning as intended?) to micro manage how states regulate businesses or go over states' heads and regulate them directly. So it would be a more or less complete 180 to see the ruling used to justify the federal government not only prevent states from regulating but allow people to go about their business without being stopped by state regulation. I think this is highly unlikely but a) it's fun to speculate and b) if the rest of 2020 has been any indication, anything is possible. Also, it should go without saying but this analysis is not exhaustive, there would be more to the issue than this.