Mary Sues make no mistakes and can do anything.
- In "Battle at the Binary Stars", Burnham royally fucks up by killing T'Kuvma by accident after Captain Georgiou is killed.
- In a Season 2 episode, "Project Daedalus", Burnham can't bring herself to kill Airiam after it's proven she's been compromised and a threat to the mission. Nhan has to do what Burnham couldn't.
- In a Season 4 episode, "Rubicon", Rillak had some doubts about whether or not Burnham would what it takes to bring in Book, which is why Nhan was brought back for an episode, to make sure Burnham could track down Book. And Book still managed to get away.
She has flaws and each of those incidents make her:
Not a Mary Sue. Mistakes and errors in judgment like this have to be the exception and not the rule. If you have officers who make mistakes and errors in judgment
all the time, then they look incompetent.
Her entire character arc in the first season, after "Battle at the Binary Stars", is about redeeming herself. Why would she have to redeem herself if everyone thinks she's great? She wouldn't.
In the second season, Spock and Burnham don't get along easily. If she's so great, she would've. And she said horrible things to Spock in their youth. If she was so perfect and great, she wouldn't have and then she wouldn't have later had regrets.
You've likely just been reciting the same thing for five years, and have been taking the thought for granted, without actually looking at things that don't favor your position. You think the other characters and the series itself think Burnham doesn't have flaws and they praise her universally, I say that's not the case.
In TNG -- which I think is your go-to -- everyone at the beginning was talking up Shelby as the greatest thing since sliced bread in "The Best of Both Worlds"; except Riker, who felt threatened. I don't remember her being thought of as a Mary Sue. But, much as I hate typing this, I guess 1990 was a different time...