I have three notes I want to make. Firstly, twice in the film they get Harry's title wrong. He is referred to as the Prince of England but his actual title was Prince of Wales until his marriage when he was made Duke of Sussex. My guess he is that they called him the Prince of England because they expected American audiences to be familiar with England but maybe unfamiliar with Wales as a country.
Secondly, Harry is about 10 generations removed from Queen Charlotte which makes him about as mixed race as Senator Warren is Native American as according to her DNA test whose native American ancestry was about 6-10 generations previous.
Finally, when her hairdressers niece asks Meghan if she will become a Princess she says yes which is technically true, but is much more complicated than she lets on. This is because Meghan isn't a Princess in her own name as she isn't from a royal lineage. She is technically Princess Henry of Wales as she became a Princess through her marriage. The same is true of Kate Middleton who gained the title through her marriage to William and was true of Diana who was never officially Princess Diana but to make things more complicated did hold the title of Princess of Wales. Lady Di was often called Princess Diana but that was never her actual title. In practice Meghan uses the title Duchess of Sussex as that's a title she holds in her own name but she wasn't granted that title until her marriage to Prince Harry. However all of that may have been too complicated to explain to the small child so I guess a simple "I am" saved her explaining the weird titles system of the British monarchy.