This is really an Ancient DNA question. As for ancient Egypt, you have this study of ancient Egyptian mummies which show a higher affinity towards Middle Eastern populations rather than Sub-Saharan ones although a "Sub-Saharan pulse" of dna flowed into the population of Egypt at a much later stage, ca 700 years ago. Modern Egyptians can trace roughly 8% of their genome to sub-saharan groups. This element seems to be missing from the ancient egyptian mummies.

https://www.nature.com/news/mummy-dna-unravels-ancient-egyptians-ancestry-1.22069

When some refer to black ancient Egyptians, they can be referring to the period of Nubian rulers who were indeed of Sub-Saharan origin i.e black although this was a relatively short window of rule. This is called the Kushite or Nubian period, the 25th dynasty. That the empire was ruled by a dynasty of Nubian leaders does not mean that the general population experienced an influx of new genomes. The same can be said for the Hyksos rulers, likely from the Levant, who ruled Egypt for a period of time although there wasn't a widespread population replacement due to an influx of migrants from the north.

The Egyptian kingdom was vast and further south down the Nile River Valley, the farther south you got you surely could find a higher prevalence of black African subjects in direct exchange with or under influence of Egypt.

There is nothing in the history records or dna wise to suggest that the earliest farmers of Mesopotamia ie the source populations for the earliest literate civilizations were of African origin. I'm not entirely sure what Mesopotamia entails in said hashtag although I am assuming it is referring to the Sumerians, Akkadians, Babylonians and Assyrians. Claiming that the Semitic speaking latter 3 civilizations were black African can not be taken seriously and frankly does not require some sort of explanation. Simple, no these empires were not black. As for Sumerians nothing can really be ruled out since we lack dna samples from individuals dating back to Sumerian civilization, in Sumer and verifiably culturally Sumerian (very tricky). They did not speak a Semitic language. A southern origin can not be excluded, possibly a connection with the Dravidian populations of the Indus valley civilization, geographically in modern day India /Pakistan. For more on Dravidians or more specifically ancestral South Indians:

https://www.the-scientist.com/news-opinion/ancient-dna-traces-history-of-south-asians-66395

A possible source population for the earliest farmers in the fertile crescent and subsequent farming populations were the Natufians. This is overkill but in short, ancient DNA studies were conducted and the Natufian subjects did not show any affinity with sub-saharan populations.

https://www.biorxiv.org/content/10.1101/059311v1

Although Carthage was geographically in North Africa, it was a Phoenician (Canaanite so think modern Lebanese or Palestinians) colony. Its population was likely a mix of local berbers, Phoenician traders from the Levant etc. In other words this was not a "black kingdom" although there were surely black subjects living in what constituted as Carthage.

I've touched on Ancient Egypt above. Although there was a Nubian ruling dynasty, and there were likely a presence of Nubians throughout the empire in various functions, to call ancient Egypt a black kingdom would be incorrect.

As for Anatolian, Aegean, Canaanite bronze age kingdoms such as the Mycenaeans, Minoans, Hurrians, Hittites, Urartians, Mitanni et cetera.. There really is no serious discussion required at all. They were not black. If you have specific questions on the aforementioned related to the OP I will try to answer them.