In the context of Herodotus' Histories, the passage very unambiguously refers to Egypt. It is important to realize the context of the quote, which is from Book 2 of Histories which concerns itself with Egypt (and to a lesser extent Libya) as Book 1 concerns itself with Europe.

Herodotus was well travelled and is thought to have spent time in Egypt. It is highly unlikely that he conflated Egypt and Nubia in this way.

Part of the context, is the purpose of the passage. Herodotus was retroactively attempting to create Egyptian origins for many Greek traditions, and in doing so to claim a degree of antiquity and respect for them. You have to understand that at the time Egyptian civilization had already been around for millennia, and that for Herodotus this pedigree was extremely important.

In his account, Herodotus includes a lot of stereotypes and generalizations about Egyptians. For example, he thought they were pious, really pious. Almost too pious. That this was not strictly true of all Egyptoans did not matter in the slightest, because it only had to match his broad claims about the people as a whole, which were partly informed by stereotypes.

So this dove story is about Herodotus' taking a Greek myth about two black doves and explaining to his audience how it is actually, really a story about how Egyptian priestesses founded this Greek cult. And that is part of a larger theory presented as fact that Greek gods like Hercules were actually, really just interpretations of Egyptian gods. And all of this to show that Greek culture was actually just as old as Egyptian culture, and that the two civilizations had shared origins.

Herodotus is speaking in terms of metaphor and interpretation, so becoming too literal actually misses the point entirely. He is also is not a completely straightforward source, because he is ultimately trying to prove his own thesis about history and the world.

However, he still obviously expected his audience to nod their heads and agree that a black dove was a good metaphor for an Egyptian woman. According to prevailing theories of the day, skin tone had to do with proximity to the Sun and the Tropic of Cancer. Any people who grew up around the southern edges of the map would be dark, regardless of ancestry, while people who lived in the cold north would grow up to be pale. People who lived around the Mediterranean (which was obviously the centre of the world) were right in the middle.

The rub is that what an ancient Greek might consider black is a bit murky and would probably depend on their experience, the type of people and art they were exposed to.

Herodotus' lived in the 5th Century, and though he was well travelled, his audience was less cosmopolitan than they would be in a century or two, after Alexander's conquests made the world a lot smaller. The average Greek would never visit Egypt, their closest interaction with the country would be well-travelled people like traders and merchants or expatriates like prostitutes and slaves. In any case, they would probably have a small sample size. Realistically, a less cosmopolitan person might only have heard of Egyptians. This is not really an environment which fosters a nuanced view of a people, it actually encourages a more otherized, binary view of foreigners. In the Greek mind, Egyptians were all pious and dark because that was what made an interesting story, those were the details that stood out.

Maybe some Greeks would consider any dark or brown complexioned person to be black. Maybe others would imagine a person of East African descent.

So even if we assume that Herodotus' idea of blackness was whatever we might visualize, he still might have been basing it off of personal experience.

Another thing worth pointing out is that multi-racial civilizations are rarely homogenous, and Egypt was no exception. There were plenty of Egyptians who looked tan and stereotypically Near or Middle Eastern. There were also Egyptians who a modern person might think looked black or European. Archaeological evidence shows that there were people with red hair, and people with sub-saharan African features living in ancient Egypt.

Although a lot of attention is paid to the 25th Dynasty of Nubian pharaohs, there were always people passing back and forth between Egypt and Nubia. At a time with no hard borders or immigration laws, and plenty of people in Northeast Africa who led pastoral lifestyles, populations blended quietly.

We know that people of Aethiopian descent blended into Egyptian society throughout history, as did people from other places. Herodotus' own account describes this occurring, and Egyptology has also uncovered plenty of examples of this.

This means that the distinction between Egyptians and Nubians, or Libyans, or Semitic peoples from West Asia, was not as concrete as modern nationality.

Are Afrocentrists wrong about the, well, everything? Yeah, absolutely. Egypt was not a colony of Ethiopia, nor was it a homogenously black civilization.

But I think it is also worthwhile to point out that Herodotus knew precisely what he was saying and that he was trying to communicate this to his audience.

As an add-on, what do you mean that there is "no trace" of Ethiopian culture in Egypt?

If Aethiopian is still being used as a synonym for Nubian or Cushite culture, then actually it really exists on a continuum with Egyptian culture as they developed more like siblings than strangers. Additionally, Egypt traded extensively with states on the Horn of Africa, such as the enigmatic Kingdom of Punt. If on the other hand you mean the modern country of Ethiopia, then technically you are correct.

Hopefully this helps!