I know this is a hot take but if you're going to use Carmen Sandiego as a character... remember that the less we know about her backstory the better. She's supposed to be an enigma, a phantom, the more we know about her motivations or origins the worse the story is going to be.
Her loud coat is a symbolic taunt to the acme forces chasing her, as if to remind them she's so competent she doesn't need to try and hide to avoid capture.