This issue of who was "black" in ancient times can be very contentious, a reflection of the racism in our society which often affects peoples' interpretations of history.
"Oh, they HAD to be black," or "Oh, they HAD to be white,"... and why? Because we want them to be one or the other.
We have to define the terms if we pursue this. What does "black" mean? Here in the USA we labor under a one-drop notion that any discernible "blackness", evidence of African ancestry, makes one "black". So, if we saw an Egyptian from 3000 years ago who was actually 1/4 African, we'd call the person "black".
Well, I had a friend who was caramel-colored, she went to Africa to visit, expected people to welcome her back home, and instead in Nigeria people laughed at her and called her "chicken flesh". To them she was essentially "white". Hmmm. so what does "black" mean?
The Bible doesn't often mention skin color because it was not an issue then. They were not in the USA raised in this color-obsessed culture. What we know about Egypt, looking here at scientific data rather than the Bible, is that the civilization began in Upper Egypt among a mixture of Nile Valley Neolithics and Saharans. Both groups were African, which is to say, "black". Very quickly Egypt became rich and powerful and attracted many migrants. and so by the Middle Kingdom, Egypt was quite mixed. Many people there in fact therefore looked a lot like many African-Americans. Many like to look at Eurasian DNA found in Egyptian mummies from the Middle or New Kingdom and then proclaim that, "See, Egyptians were just like today's Arabs or Berbers." But of course they're ignoring Egypt's origins and the changes which were always occurring as more people came into Egypt both from Eurasia and from the South (Africa).
As for Israelites, the same dynamic applies. They enter history already mixed, like many of the Semites of the Levant and Mesopotamia. Some of their ancestry did come in from the north. The peoples in the various hills and mountains of the "Fertile Crescent" were quite diverse, from the Zagros Mts. to Anatolia and the northern Levant, but all of Eurasian types. Likewise, there was migration out of Africa, especially through Yemen, of "black" people. so that today in southern Arabia genetic studies show the population to be of 22% African descent. The Israelites, as well as the other Semites, therefore had African admixture in their population.
So... who was "black"? If we went back to the time of the Kingdom of Israel, we'd see many Israelites whom in the USA we'd call "black". Most would have looked like what we loosely term "Mediterranean" today... like Greeks, Moroccans, Lebanese, etc.
To anthropologists "race" is interesting only as it indicates migrational history and mixing of various groups. What really identifies people is their culture. Again, in the USA we've a confused view of this, since 2 of our ethnic groups are named after colors (black anad white)! And so, in the USA we are often confused about all of this, not understanding that ethnicity has nothing to do with race, really. But for both of these 2 groups, ethnic ancestry is very mixed. Whites are Scottish, English, German, Irish, Italian, Dutch, etc. Blacks are Yoruba, Bambara, Mandinke, etc. Then in Virginia in the 17th century the categories "black" and "white" were codified, creating an oppressive social division (which worked against working class whites as well as blacks) and engendering an obsession with color which is still with us, as evidenced by the intense arguments over whether Egyptians or Israelites were "black" or "white".
The joke's on us, since most Israelites in ancient times likely wouldn't quality as "white" even if they weren't "black". So... what was Jesus? Answer: He was a Jew.