Citation needed.
Per
Wikipedia:
A Mary Sue is a character archetype in fiction, usually a young woman, who is often portrayed as inexplicably competent across all domains, gifted with unique talents or powers, liked or respected by most other characters, unrealistically free of weaknesses, extremely attractive, innately virtuous, and/or generally lacking meaningful character flaws.[1][2][3][4][5] Usually female and almost always the main character, a Mary Sue is often an author's idealized self-insertion, and may serve as a form of wish-fulfillment. Mary Sue stories are often written by adolescent authors.[6]
Michael Burnham is not "inexplicably" competent -- like every
Star Trek protagonist (except Dal from
Star Trek: Prodigy), she is a graduate of an extremely prestigious institution of tertiary education (the Vulcan Science Academy for her, Starfleet Academy for all the others), and has already had a long career in Starfleet when the series begins.
Michael is not competent across all domains. She is a competent science officer and pilot, but she is not an engineer or doctor.
Michael is a gifted leader, but she does not have special powers.
Michael starts off resented by most of the other characters and only gradually earns back their respect. Even as a captain, there are characters who have serious problems with her leadership style and choices.
Michael is attractive to the level that most
Star Trek characters are attractive; she is not a supermodel or unusually attractive within the world of the show.
Michael is clearly not innately virtuous, given her actions in the series premiere.
Michael has meaningful character flaws throughout the series, including arrogance, aggression stemming from trauma, early difficulty respecting other people's emotions due to her Vulcan upbringing, refusal to acknowledge the limitations of her own power to protect others (another manifestation of arrogance).
In short, Michael meets none of the traits necessary to constitute a Mary Sue...
except that she is a female protagonist.
Which is not the case with Michael. She can be a selfish asshole and she made horrible choices that got people killed out of arrogance and trauma.
