Congress' power to naturalize is unlimited, period.
The naturalization power is referred to in the second part of the first sentence of the 14th amendment, but the power to naturalize is not conferred there.
Art IV, Sec. 2 (citizen of a state) is not about naturalization - those persons are citizens without being naturalized.
The first part of the first sentence of the 14th amendment recites, in part, "born in the US ... and subject to the jurisdiction." Those persons are not naturalized either.
And that is where you are going wrong. The authority is NOT "power to naturalize" the authority is "To establish an uniform Rule of Naturalization". That is FAR MORE than just the power to naturalize.
The rule of naturalization includes:
Rules that govern who is able to be naturalized
Rules that govern who can never be naturalized
Rules about how to apply for naturalization
Rules on how citizens give up their citizenship
Rules on the process and procedures on how an alien becomes naturalized
Rules on who does not need to be naturalized
Rules on who is a citizen at birth by the circumstances of their birth (naturally born a citizen)
Congress authority to naturalize seems to be very limited. Congress unnaturalized the nation.