States have authority to do whatever they want provided it is not already defined by the US Constitution as a federal power.
Whatever they want? That strikes me as a bit of an overstatement.
But be that is it may, I still question governments at any level have the legal authority, other than assumed de facto powers, to set wages. In fact the first attempts in this country to establish minimum wages on the state level was declared unConstitutional in the early part of the 1900s. But then along came the New Deal and in 1933 we got the first federal minimum wage which was once again declared unConstitutional, then reinstated for good in 1938.
From this poisoned root came all the minimum wage laws which followed as governments everywhere, state and local, decided under force of law to establish wage policies for everyone under their authority. The whole concept is divorced from any sense of property rights and economic realities in favor of pandering to the electorate and, as usual, soliciting votes for themselves.