Burnham certainly IS a kind of Mary Sue.
Despite her f*cking up big time in the pilot - what she did was always the right choice, she was just wrong about the specifics on how to proceed. Since then, she has been shown to be a master at... everything:
-Chemical/Physical science, hand-to-hand-combat, outsmarting everyone else, creature care, coming up with clever new plans on the spot, always taking the ethically correct choice... she's perfect. And everybody is always telling it her - Georgiou (both!), Lorca, Saru, ... everyone. Also, everyone is always falling for her to such a degree they're sacrificing their own plans just to 'get her' - both Tyler and Lorca get foiled by how awesome they think she is!
But you know who else has all those characteristics?
James T. Kirk.
Will Riker. Sisko. Janeway. Hell, even Archer at times.
Yes. Burnham is a Mary Sue. 100%, undeniable. But you know what? It's a Trek staple. The main character always is. The only difference seems to be that women (Janeway, Burnham) get critizised extra hard for it.
So far, it doesn't bother me. But if someone is put off by it, that is completely justifiable, because she is a Mary Sue. But by FAR not as much as the ultimate Trek hero: Kirk.