Go ahead and address the issues you raised above - that English common law actually supports Vattel on “natural born”. Your only statement so far is the obvious one that English and American common law diverged.
To myself and to you, the statement appears to be obvious. The same statement was vehemently and discourteously denied in another very recent thread. So, not taking anything for granted, I'm trying to proceed one step more or less at a time to identify the points which can be agreed upon or remain disputed.
Next, the American common law diverged significantly from English common law immediately upon the establishment of each English colony, each non-English colony, and their colonial governments. By the time of the Constitutional Convention and the adoption of the Constitution, American common law reflected its own native innovations and contributions from the English, Scots, Irish, French, Spanish, Dutch, German, Danish, and Swedish legal customs, with apologies for any neglected.
Meanwhile, the English common law had undergone significant changes before, during, and after the establishment of the North American colonies.
Likewise with the civil law/s of the other colonial powers, they too underwent significant changes before, during, and after the establishment of the North American colonies. The laws regarding citizenship were among those laws and customs which underwent the changes before, during, and after the establishment of the North American colonies.