“So we are all naturalized now?”
No.
“That language represents the first prong in the 14th amendment.”
The 14th Amendment has no more power to alter Natural Law than does the original Constitution or any other form of statutory law. The Constitution and the 14th Amendment can do no more than recognize the inherent Natural Law, as they did with respect to the Law of Nations and the Bill of Rights recognizing the inherent right to free speech, right of assembly, and right of self defense. Consequently, the 14th Amendment pertains only to the Constitution’s grant of power to Congress “To establish an uniform Rule of Naturalization.” Naturalization of course means to take an alien person and MAKE the person a naturalized citizen for the purposes of including a foreign born persons into the same community as the natural born persons.
NBC is a legal term of art. It's not expounded in the constitution, and while a statute could express what NBC is, what NBC is does not depend on the existence of a statute. Same goes for "citizen" other that of the naturalized sort.
I agree with your conclusions, but the text of the 14th amendment doesn't get us there. IIRC, it was said that the 14th amendment has ZERO effect on the meaning of NBC. The 14th amendment operates to prevent states from excluding people (slaves, mostly) from US citizenship.