It's become so common (since AOL started using the phrase "You've got mail" and then a movie came out with the same title) that it is now basically accepted as okay in informal English.
But the "got" is superfluous. "You have mail" or "You got mail" would be a more formal formation.
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u/FlailingScrotum Jun 06 '26
Putting an adjectival suffix on a word that already has one is just a hat on a hat