I agree with you. He seems to be confusing unity with equality. This statement
Olusoga pinpoints 1973 as the "high water mark" of UK equality
is complete nonsense. Just try being a woman, gay, black or even Irish in 1973 and you'll understand the meaning of inequality.
I agree that Brexit was the most fractious recent moment rather than the Scottish independence referendum. Scotland voted for the union in the independence referendum and that would have been the end of the matter for a generation if it hadn't been for Brexit. The Brexit divisions were not "nation from nation" but the divide split us in a way that was not strongly related to nation, class or politics. Brexit made me realise that I share my country with quite a lot of bigots and racists and it empowered them to declare their bigotry in public.