Then there can be the constitutionally mandated federal district, that consists simply of the federal buildings, and everywhere that people live (outside of the White House, Number One Observatory Circle, and maybe a few other formal federal residences) would actually be within state jurisdiction.
This already happened to the bulk of the Virginia side of DC in 1847 (https://en.wikipedia.org/wiki/District_of_Columbia_retrocess...). I don't see why they don't just do that again with the rest.