The same people have always lived in Egypt.
The ancient Egyptian individuals in their own dataset possessed highly similar mtDNA haplogroup profiles, and cluster together, supporting genetic continuity across the 1,300-year transect. Modern Egyptians shared this mtDNA haplogroup profile, but also carried 8% more African component.
The ancient Egyptians were more related to Middle Eastern people than modern Egyptians who are more related to black Africans, but overwhelmingly the ancient Egyptians are the ancestors of modern Egyptians.