This is as good a place to star as any I suppose. Let's start with a trusty Google definition:
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This definition is more concise than the ones put forth in the articles you provided and I think it is more in line with how people are using the term. The historical development of the term is interesting, but I think the term has moved well beyond that. Being a sort of "unofficial" term, variations in its usage and meaning will vary. For instance, in the following video (which is admittedly a singular person's opinion), a Mary Sue is defined along 7 variables:
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The original video can be found
here
Personally I feel that 6 these categories are pretty spot on. I would argue against the "No Personality" category on the principle that I don't quite equate it necessarily with a Mary Sue (meaning a Mary Sue can still have a personality) and also that Rey (and Luke) both have a personality.
So with that, some of the key aspects of a Mary Sue (as the term is typically used in a modern day context) revolves around any iteration of the following traits:
- Overpowered/Unexplained Power level (I think these two are inter-related)
- Perfectly good (sometimes a few quirks are thrown in, but they are always minor and insignificant)
- Instantly liked (or near instantly liked without sufficient justification)
- Feels like wish fulfillment (enter the Disney feminism & identity politics push)
- Character barely experiences failure/low-points/embarrassments (as with the "perfectly good" criteria, a few minor or insignificant setbacks can be thrown in here)
People might employ slight variations to these categories and nor are all the categories equally important, but for the most part I think this is a fair assessment. I don't think anybody cares about the character's eye colour or clothing style when assessing Mary Sues. Even if those items were historically linked with the term, they are pretty much irrelevant when used in today's context. If you want to argue semantics that is a different story, but the fact remains that Rey fulfills all the
core principle elements of a Mary Sue.
Really. Han offers her a job literally 5 seconds after learning her name. He gives her a blaster, not out of self-preservation but because he is looking out for her. In the entire scene it is evident that he already likes her and is looking out for her as a father figure.
Stormtroopers are too stupid to fear anybody for the most part; they are pretty much cannon fodder. You are correct that Snoke didn't fear her, it's a shame that he has been removed from the series. Kylo begins to fear her pretty quickly...
Now is the fear "instant"? No, but close enough. Here you also see an example of her demonstrating her unearned OP abilities. Although she has great potential in the force, she is completely uninitiated at this point and should be easy prey for Kylo who should be significantly more advanced than her (as he trained under Luke AND Snoke; and has Skywalker lineage to boot!)
Firstly I would argue that this not really important in assessing a Mary Sue. That is not a core criteria in the way the term is used today. Also, the nature of Star Wars (family friendly series) pretty much makes this an impossibility
Snoke making her look the fool is about the closest thing she has to having a set back. Like I've said previously, Snoke was an intriguing character but he has been removed. Even then, the setback is inconsequential and short-lived. She loses nothing in the interaction and the situation quickly resolves itself (and not by her overcoming it as you suggest, and thank god for at least that)
Learning her parents were nobodies is perhaps an emotional setback, but it is not due to a failing or lack on her part. She has zero control over it. She didn't fail in that situation. Also as a side note, we don't actually even know this to be true. This is what Kylo is telling her. I could be wrong, but I wouldn't be surprised if the whole situation with her parents end up being something else entirely.
Han dying is hardly her failing as well. She wasn't involved in that scene other than to react to it. That was between Kylo and Han. It is Han's failing (or Kylo's, from a certain point of view *pun intended*)
Luke not training her is the worst example of them all. That is just a prime example of the dumpster fire that Rian Johnson turned Luke into. That is a failing of Luke not Rey. What's worse, it turns out that she doesn't even need Luke's training, she is perfectly fine without it (because of the supposed download from Kylo's mind during their mergers). She swings a lightsaber at some rocks and all of a sudden she is able to school Snokes elite guard.
Not one of these examples exhibit a true failure on her part with any real or lasting consequences.
The other characters that came before had to
earn their abilities. Everything is just handed to her on a silver platter by the SJW writers.
Rey thinks up a solution on the spot to fix the Millennium Falcon that completely surprises Han. Han, who has spent most of his life time flying, fixing and modifying that ship. Nobody should know its systems better than him.
Rey also masters flying the Falcon within minutes of first stepping foot on it.
Rey (as you eluded to) masters the Jedi mind trick, without any training or experience. How did she even know about it, let alone know how to do it?
As for her lightsaber skills, she is gifted those pretty quickly as well. Her "training" in Ahch-To is a joke. She swings around her lightsaber aimlessly and we are meant to think this somehow constitutes as training. Luke in no way instructs or demonstrates its usage to her.
Kylo should still have been able to beat Rey. Even injured he should have been able to easily defeat her. She has no experience with the weapon or with the force. He has been trained by two masters (Luke and Snoke). He should have been able to cut her down in seconds. Not only that, but she was able to out use the force against Kylo by pulling the saber to her hand when he was trying to do the same. How did she learn to do that, and how did she surpass him so quickly?
Read the Darth Bane trilogy, there is a scene where Bane is wounded (far beyond that of of Kylo) and read how the Dark Side can be used to overcome such a predicament. Now Kylo is obviously no Darth Bane (nor is any of the Disney stuff anywhere close to the quality of the Darth Bane series) but the point still stands.
Obviously she can't stand up directly against the Prequel characters who have been trained since a young age by the greatest masters in the galaxy under a system that had been developed and honed for thousands of years. However, for her relative level of training/experience she is far above any of them. She masters things without training that would take them many years of study/practice to grasp. Her rate of learning is far superior to any of them (including Anakin).
As for her force abilities being underdeveloped, are you kidding me?

She has no training and she is able to complete feats that are beyond trained users.
She is able to telekinetically overpower Kylo and draw the saber to her hand (without ever being trained to do so).
And then there is this little gem. Probably the worst example of her overpowered force abilities...
https://www.youtube.com/watch?v=UYxlpbbHhvI
Now compare and contrast this with Luke learning to do the same thing (with more training)...
https://www.youtube.com/watch?v=5-Gen_qheOo
Notice the difference? She has less training than him and easily completes the task while he struggles and fails at lifting a few small rocks one at a time. Her lifting all those heavy giant stones is probably one of the greatest (if not the greatest) demonstration of that particular skill in the films, consider both the weight and number of the boulders she is manipulating (without even looking that concentrated or stressed). Even Yoda (with hundreds of years of training and experience) cannot preform the feat as easily. He has to concentrate when lifting the Xwing out of the swamp and also when preventing the column from crushing Anakin and Obi-wan after the Dooku fight.
Because the prequel characters have
earned their abilities. Training, experience, guidance, failure coupled with learning... rinse and repeat across decades. There was an entire organization that had slowly developed proper training methods to develop such skills. Training classes, mentors, Masters, the Jedi library. I'm not sure how you can even equate the two.
Rey just gets it almost immediately without all the preparation and suffering that should come before it. We should all be so lucky, no need for schools, books, teachers, practice or coaches.