There’s a funny story about this idea that may be an urban legend:
I think Americans of a certain age learned the term as a replacement for ‘black’, or whatever the previous favoured word was, so that’s how they used it. But Americans forgetting there is a world outside the US is also something of a meme.
It still doesn’t include Mamdani.
Tell that to all the white women who got in big trouble for identifying as Native American (and not as full members of a recognised tribe, either).
I get the impression this is a major reason establishment Dems don’t like him - they think he’s going to mess up and make the party look bad.