Mary Sues are perfect and infallable. Kirk had some spectacular disasters on his watch, and admitted to Spock he was out of his depth and just doing his best.
Burnham fucked up too, with her botched mutiny and then revenge-killing T'Kuvma when taking him alive was her idea.
Mary Sue's are also self inserts of the writer.
Wesley is closer to a Mary Sue than Burnham is.