I notice the 'Mary Sue' term rearing its head here quite a bit, with someone even claiming that Kirk is a 'mary sue' character.
A 'mary sue' is when a writer effectively writes themselves into the story in the form of a new 'secondary character', but in such a way that they overshadow the main characters and become the central piece of the narrative. They commonly solve all the problems, give advice to the main characters, romance the main characters, and know more than the main characters when they shouldn't. In the end, they often save the day, relegating the regular cast to the sidelines. A 'mary sue' is essentially a writer making themselves (by proxy of their character) the unlikely hero of the story.
Kirk and Spock were the main characters of TOS, so by that yardstick alone they cannot be considered mary sue characters.
Chapel is an established character from TOS, and she isn't written by any one writer. The writers can be accused of 'over-writing' her, or giving her mary sue elements, but aside from a couple of egregious lapses (killer combat kung fu girl on popeye juice), she largely stays within the lane of her position and abilities. The romance stuff with Spock has been atrocious, and her being sole survivor on the Cuyoga was pure, story-breaking plot armor that was only needed because the writers wanted to touch your Spock/Chapel feelies in the finale. But a mary sue? Not even close.
Side note: The Cuyoga situation would have been much better handled and much more believable if Chapel had stayed on the surface with Batel, been rescued from there along with Batel, and Enterprise had simply scanned 'no survivors' before Spock iced the Gorn and sent the saucer plunging into the beacon.
But, anyway. TLDR: You keep saying 'Mary Sue'. I do not think it means what you think it means.
As we both admit that the Cuyoga situation was bad,it prompts the case that she is a mary sue in that moment. a mary sue is a character who tends to be special for no real reason or no good explanation. The writing could have been better if Chapel explained how she survived when others did not. Chapel been the lone survivor of the Cuyoga makes her special or different for no reason. She scores here as a maru sue.
The notion that we can admit they needed to make the Cuyoga more believable is what makes her a mary sue because mary sue characters tends to have little realism to be believed. Mary Sues also tend to be in poorly written romances, the mary sue’s partner will act out of character just to please her and not make her take any responsibilities of some of her own short comings.
Spock acts this way when he says he wants to apologise to her even if from the audience’s point of view, Chapel was the one who hurt him more. From the little we saw in the romance, Spock did try to help her but she kept on blowing him off until the public break up. These are mary sues symptoms we see in Chapel and in the romance.
