'Enslaved people' foregrounds the humanity of those who were owned by others. 'Slaves' puts them into a separate category.
I think that 'white supremacy' is appropriate in this context. I think that Avalon is proposing that not all 'whites' were supreme. I take 'supreme' in this context to mean that their interests, power and way of life takes precedence over everyone else's. Which, for a certain section of the white population, it clearly did.
The idea that not all white people were 'supreme' is often confused with the term 'white privilege', which people then object to because, as we know, white people have been systematically oppressed in the past, and still are. I am a member of a lot of local history groups, and nearly every day someone will post a photo of ragged children, with the caption 'so much for white privilege' and there follows a stream of rants about how black slaves often had black overseers, or were sold into slavery by treacherous Africans, or how bad the conditions in mines, mills and factories were in the past. It is as though the fact that white people often have hard lives negates the notion of racism, when they can, and do, both exist at once.
White supremacy and white privilege are not the same. White supremacists are those who believe that white people have a fundamental right to rule over non-whites because they are intrinsically superior. They are likely to support apartheid, colour bars and so on.
White privilege is the idea that white people, whether they are in a position of financial privilege or not, start most interactions from a position of relative ease. They don't get routinely stopped by the police. They don't have to explain where they 'come from' as though they are foreigners in their own country. They take for granted that they, and people like them, will be represented in drama, adverts on TV etc, without there being a storm of protest. They aren't accused of 'playing the race card' if they speak out against injustice. Etc.
The privilege is not having to wade through that lot before you even start, and there being very little chance that the person you are applying to work for will take against you because of your skin colour, or that someone will not want you as a neighbour, or any of the day-to-day micro-aggressions that many POC come across all the time.
Obviously I can't be sure what Avalon meant in her OP, but using the example of Scottish mine owners being oppressors (and of Scottish miners being exploited and ill-treated) as a way to question white supremacy doesn't seem logical to me.