Yet for some reason the Governors of the States have to sign a bill and can veto the Legislatures election Bills. Do you ever wonder why that is, or think perhaps the Legislature don't have the authority you think they have?
Read the Constitution.
We've already had lengthy discussions on this topic. Read them, too.
I don't have the time or the inclination to tutor you.
You obviously don't know what you think you know. The term "Legislature" in the election clause has been broadly interpreted as being the law making apparatus of the States.
Duh!
The legislature of a state does not include the Governor, Lt. Governor, Attorney General, Treasurer, or any other officer of the state. It includes only elected Representatives and Senators whose duties are to propose and either reject or pass bills to be sent to the Governor for signing into law.
That procedure is exactly what happened regarding the recent Georgia election reform law.
Can you provide a link to your apparent claim that the term
legislature includes anything other than the two Houses of Congress that exist in the states?