> They are given a lot of latitude in how they run elections, limited by state law and state constitution edits that are also controlled by state legislatures.

State Constitution changes are often controlled by the people, ultimately, not the legislature, which has occasionally been used in Presidential election cases to argue that such State Constitutions cannot constrain regulation of state elections because they are not under the exclusive control of the legislature. The federal courts have, IIRC, consistently and emphatically rejected this logic, though.