NYC is not 13,318 sq mi which is what your talking about aka an area ~200 miles wide and bigger than the state of Maryland. By comparison DC is 61 square miles total your figure is like lumping DC, Baltimore, and Richmond VA into one metro area.
Not really: "It is composed primarily of two major metropolitan statistical areas, the Washington–Arlington–Alexandria, DC–VA–MD–WV MSA and the Baltimore-Columbia-Towson, MD MSA. In addition, six other smaller urban areas not contiguous to the main urban area but having strong commuting ties with the main area are also included in the metropolitan area."
I mean some people talk about the Northeast megalopolis. https://en.wikipedia.org/wiki/Northeast_megalopolis Boston, New York City, Philadelphia, Baltimore, Washington DC, and some times Richmond. But, that does not mean Boston and DC are somehow the same city.
https://en.wikipedia.org/wiki/New_York_metropolitan_area