What kind of governments did state constitutions create?
It depends on the state, but most have a similar three branch structure to the US federal government.
If we're talking about the first 13 states, the state governments did a lot to inform the framers of the US Constitution in creating a three branch government, not the other way around.
A good number of states had an executive in the form of a governor, a legislature that often was bicameral (two houses), and a judiciary in the form of a state supreme court.
Massachusetts and Virginia both fit this bill. This is notable because their constitutions were instrumental in guiding the "Founding Fathers." (And, of course, many of the same people who drafted state governments were involved in the drafting of the Constitution.)