Miles is naturally more outgoing than Peter, as evidenced by his larger friend group at the same age. A mask isn't going to make him further lose his inhibitions like shy Peter, and it's not going to make him quiet just because the situation is serious. I don't think it's a big deal that his personality is more consistent. That's the case for most superheroes. For example, Captain America and Ant-Man don't show different sides to their personality because the mask is on. Trying to force a dichotomy on Miles might end up making his psychology less believable. Also, Miles was more awkward in Spider-verse while under the mask because he was even more out of his depth than usual, but he's awkward throughout the move, with or without the mask. He's still clearly figuring out who he is.

If there's a distinction between the Miles and Peter spider personas, besides their ages, I would have it be the style of their humor, with Miles having a Ben Grimm/John McClane sense of humor, while Peter has a Johnny Storm/roast the villain sense of humor.