I understood that the "black" Dynasty was rather later, during the Third Intermediate Period?
Yep.
BTW, if you want a reasonable overview of the TIP without too much paracetamol, try "Afterglow of Empire" by Aiden Dodson.
The twenty-fifth dynasty was the one where Nubian kings had a takeover bid, with a curious blend of African anf Egyptian cultures.
Before that time, though, settlers had been filtering into Egypt from Lybia, Palestine, what is now Asia MInor, and Greece, for centuries - even as much as a millenium. Kings married foreign wives, and the resultand offspring made it to high office at court - even becoming kings in their own right.
The 'official' portrayal of the mighty, racially pure, Egyptian ruler beating sevwen kinds of ---- out of Jihnny foreigner, which appears on temple walls by the dozen, was often far from reality.
Even Tutankhamun, through his grandmother, great grand mother(s) etc, was probably not 'pure blood Egyptian.
A lot of black people from the States (no surprise there, unfortunately) try to invade various Egyptian groups on FB claiming every single Egyptian was 100% 'African'.
When we point out that race didn't seem to bother the Egyptians, they throw a hissy fit.