For me the important thing is: What did the term mean in early America?
A lot of commenters in early America said you had to be "born in the United States" (note the lack of any mention at all of citizen parents) in order to be eligible.
I think this was just a bit sloppy, because they ignored those born US citizens abroad, who were also eligible.
And some other commenters noted specifically that such people were eligible, including James Bayard in his exposition of the Constitution.
Many commenters stated, more accurately, that you needed to be "born a citizen" or "a citizen by birth."
See the discussions in posts 199 and 226.
And for all of the important quotes on what our Founding Fathers and Framers actually said, including a mention of most or all of the very few people who thought otherwise, see this post.
Anybody that follows one of your links is wasting time that would be better spent doing anything else.