After doing research on arguments about weather or not Batman is a Mary Sue (I personally don't consider the term gender specific. Also Batman is another subject for another thread), I eventually found the TV tropes page here:
Honestly, I thought that some of the suggestions went beyond preventing a mary sue and risked pushing your character into background/filler character territory.
"Spotlight-Stealing Squad is another no-no. Even Canon characters are often considered Sues for this (like Wolverine), and it goes double for fan fiction. The main characters are where the focus should be. Keep it on them as much as possible. That way, where there are scenes that need to focus on your character (the introduction of your character, any Character Development scenes), they will make sense"
My problem with this is, particularly the part in bold that if you take this advice too far, your just telling the same story with 1 more background character and nothing really changes.
If another character is The Chosen One, that character stays The Chosen One. Your character doesn't become the new one instead (unless a story has that happen all the time, like Slayers on Buffy the Vampire Slayer and Avatars on Avatar: The Last Airbender). Now, if your character is chosen for something else, preferably a lot less significant than a main character, you could get away with that. Or your character could be destined to play support staff, like Taking the Bullet or something similar.
I feel like this is also bad advice. Some people don't like a given canonical chosen one and can make a great story out of replacing them. Some might be trying to write a "what if" fic with a different cannon or non cannon character chosen.
Don't have your character save an entire society; play it safe and leave that to the main characters (although as has been mentioned, your character can play support staff).
Honestly this is starting to feel like anti-OC bias here. If the OCs cannot be allowed to add anything to the story then whey are they there?
If a canon character is noted as being the last of his or her race/species, especially if this is a major plot point, don't introduce a previously-unheard of family member who is the real last one standing. If you want to write a character like this, consider making your story a Prequel, set before all the other of the canon character's kind died (though this will limit your story options: you likely won't be able to use other canon characters that weren't encountered until the present timeline, for example, and going this route means by definition that your character will have to die at some point).
I think this should come with a corollary that this isn't an issue if you can plausibly explain why there is another survivor. For example, what if Kalel wasn't the only Kryptonian to be launched into space? In https://www.imdb.com/title/tt0115378/ Superman the Animated Series, after Krypton blew up, a neighboring planet's ecosystem started to destablize. Canonically super girl is from this neighboing planet, and Superman finds her in stasis years later. It wouldn't be too much of a stretch for someone else to have the same idea as Superman's parents did.
The following complaint may come from me enjoying the often ridiculed genre of "fix it" fics, crossovers, self inserts, or any combination of those traits if they are written well: Another issue I have with a lot of advice in this article is that what if the point of the fanfic IS to change the story by adding another character and thus causing the butterfly effect?
For example, read this:
Then ask your self: "what would happen if the new character was a normal early 21st century human instead of a Commander.from Planetary Annihilation?"
If the point of the fic is to change the story, then your OC should have enough power to do it. This is where I feel the anti Mary sue pressure hurts most of all.
This is not to say that all of those marginalized genres I mentioned are actually good all the time. Like any genre, there are good and bad examples:
I once read a fanfic that I can no longer find where the OC is a human inventor who makes a teleporter that lets him go to the world of sonic the hedgehog. When he arrives, he beats Knuckles in a fist fight, boasts that he was holding back, then randomly and inexplicably is a pokemon trainer and has pokemon with him 1 chapter later.
As for one example of a good self insert butterfly effect story:
I also recommend https://forums.space...ross-si.368095/ (same link that I posted above) as a good "the plot changes course" via the OC's powers example
and https://www.fanficti...o-if-you-please As an example of how adding a new power that none of the canonical Stargate characters have can still make a good story.
Of course, this is my opinion and I'd like to hear yours