True, I mentioned “casual googling.”
Not sure what you mean by that. Whatever the ethnicity of Greece might be claimed to be is hard to say given the history (which Greece exactly?), though contemporary academics tend to mention that old Victorian and earlier romanticizing was in many ways a pretext and justification for cultural imperialism, and whatever the ancient Greeks looked like, they definitely weren’t the pale northern Europeans they are often mis-portrayed as. What the Greeks are notable for are artistic, intellectual, political, and cultural developments that had nothing to do with the color of their skin, and the later cultures who adopted some of their better (and worse) ideas were ethnically distinct. Much of the talk of contemporary scholars on race is to dismiss the ideas you’re suggesting they’re proponents of - there’s a now lot of pages spilled detailing the sources of the cultural borrowings by Greece, including the Egyptian influences on Minoan, Mycenaean, and early Greek art and architecture (and math). That romanticizing you mention is something modern academics actually take great pedantic delight in ripping into even if it persists in the popular imagination and terrible movies - subverting cultural hegemony something is something many of them have as a hobby given that they work in Humanities departments.
Rome at its height was a massive multi-ethnic empire. If you go back to the early Republic there’s more homogeneity, but even then the whole idea of the project was to band together smaller political entities through contractual obligations for a claimed mutual benefit without any interest in ethnicity (which quickly expanded into militarist conquest, though they preferred contracts to legions). They didn’t have the modern idea of race, accepted/conquered people into their political alliances regardless of their skin shades, intermarried a lot, and wound up with many African Romans, some who rose to great prominence, among the notable being emperor Septimius Severus, Terence, Apuleius, Tertullian, and Augustine. Since Romans didn’t have the modern idea of race they didn’t really note people’s ethnicities unless they were trying to slag some foreign group they were at war with, and then they were more likely to be flinging crude stereotypes at Celts or Germans than sub-Saharan Africans. The Romans were very tribalist, but they had no modern notion of race. Romanness, whatever it meant, was never about being pale skinned (esp. since the original Latin peoples who founded the city weren’t), and there isn’t anything you could reasonably call an ethnicity of Rome.
I can’t say what ancient Egyptian skin color looked like, but I will say that I am very sure that if contemporary scholars who look into the matter currently believe that the Egyptian populace was a mix of different groups with different skin tones or whatever, they do so for reasons other than institutionalized racism. I knew Egyptologists in school and did some classes with them - they aren’t at all who you think they are, their motives and approaches to research aren’t what you think they are, and your ideas about what they do aren’t accurate.
Regardless, even if your ideas about Egypt’s race and influence were completely correct, the way you approach the problem reifies racism and propagates the problem I assume you’d like to solve - racism is based on fundamentally ignorant ideas about what it means to be a human being, you can’t solve that by dwelling on the race of some people from a few millennia ago.