So, what does "Residence" mean to you, then?
The meaning of that word isn't in dispute.
"All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside."
The "wherein they reside" portion pertains to the state citizenship. They are citizens of this state or that state, depending on where they reside. It does not pertain to the United States portion.
Because you are a citizen of the United States, if you live in Texas you are a citizen of Texas. If you move to New York you become a citizen of New York.