There is nothing in the federal constitution that precludes a state from making election laws and rules. In fact it effectively requires states to make law and rules.
This approach, to say the least, is not how the Constitution has been understood in the past. Previous decisions define the word “legislature,” when used in this context, to refer to whatever the valid lawmaking process is within a state. As the Supreme Court held most recently in Arizona State Legislature, the word “legislature” should be read “in accordance with the State’s prescriptions for lawmaking, which may include the referendum and the Governor’s veto.”
https://www.vox.com/2020/11/3/21546419/s...h-carolina
This approach, to say the least, is not how the Constitution has been understood in the past. Previous decisions define the word “legislature,” when used in this context, to refer to whatever the valid lawmaking process is within a state. As the Supreme Court held most recently in Arizona State Legislature, the word “legislature” should be read “in accordance with the State’s prescriptions for lawmaking, which may include the referendum and the Governor’s veto.”
https://www.vox.com/2020/11/3/21546419/s...h-carolina