She is not a Princess. I think if he were the son of the Soverign, it might be different?
Meghan became a princess of the United Kingdom upon her marriage to Prince Harry. Officially, she is known as Her Royal Highness The Duchess of Sussex, Countess of Dumbarton and Lady Kilkeel, but she has elected not to use the style of Her Royal Highness.
She is a princess by marriage, which means that she is not in the line of succession.
Part of the Mexit agreement was that Harry and she would not use the “Royal Highness” styles, but they would be allowed to keep their style and titles.
However, the Oprah interview might be seen as breaking the Mexit agreement.