First, she reached out and moved the black woman's hair so she could see her nametag.
Haven't seen that footage but ok, dick move.

In what universe do you go do that to someone you don't even know? Only in some colonial world of yore, not today's world.
This leap in logic is not helpful. If she's this kind of person, do you think she's treating me with any more respect? That you assume colonial racism because she's working for the royals, that's no better than applying stereotypes to others.

Then, she hectored her for a good five minutes about "where she was from, where are her people from etc.."
How do you know this? Is there footage of this because I need to see it. Having a five minute conversation with someone who is not enjoying the conversation is tedious and obvious. Especially if the entire five minutes is the same question rephrased. This is not believable.

She wasn't satisifed with the answer "I'm from Britain," and the implication of continuing is to ask is that she's an outsider.
I'm giving the old lady the benefit of the doubt in assuming that Fulani attire is what inspired this line of questioning, not the perceived idea she's an "outsider". If I wear a red and white striped top, a beret and carry a baguette under my arm people might think I'm from France, and might be confused when I tell them I'm from Solihull.

That's the kind of question this woman has probably been asked all her life - and it must get old.
If she's been wearing Barbadian attire all her life while living in Britain, then it would not surprise me if she was regularly asked where she's from.

The point is, it's not appropriate to keep after her after she already answered the question.
I might be willing to agree with you here, but I really need to see the footage that you clearly have seen, that shows a five minute and one-way conversation.