Again, what you have described is not what a Mary Sue is. At it's most basic definition a Mary Sue is an author inserting themselves into the story. That is why a Mary Sue is almost always a previously unknown character in a franchise with existing main characters, created by an author who becomes integral to the success of whatever quest the existing main characters are on and they literally have no flaws and are perfect with everything to the point of making the main characters incompetent. That's precisely what the actual fan fiction Mary Sue character who originated the term was. If Burnham was suddenly inserted into the adventures of Kirk and Spock on the Enterprise in the 2260's, and was solving all their problems or whatever, the mary sure argument might have some basis.
Burnham has shown time and again how flawed she is. Every success Burnham has had has come because of the help of others. As example, Burnham couldn't have beaten Osyraa without the help of the bridge crew, She couldn't have survived in the 32nd century without Book, She couldn't have travelled to the 32nd century without the help of the crew and Burnham wasn't the one to figure out how to escape the mirror universe.
Kirk isn't a Mary Sue either, that guy was flawed as fuck. If you want to see what an actual flesh and blood Mary Sue is, try Captain Garth from Axanar.