Mary Sue is a defined thing, and it's very much in line with Thursday's comments.
From Wikipedia,
"A Mary Sue is an idealized and seemingly perfect fictional character. Often, this character is recognized as an author insert or wish fulfillment. They can usually perform better at tasks than should be possible given the amount of training or experience. Sometimes, the name is reserved only for women, but more often the name is used for both genders. A male can also be referred to as a Marty Sue or Gary Stu, but Mary Sue is used more commonly."
The problem with this Mary Sue argument in Star Wars is that it doesn't reflect the original trope. Mary Sue characters were (and still are) author inserts who make no mistakes and have all the best and most important abilities to perfectly defeat/overcome their obstacle. If you want to see a very recent example of this, I give you a Top Post from r/Overwatch that, while very well designed, is very much cringe and self-insert.
Thing is, this trope treads very closely to superheroes and Chosen One archetypes because typically their only conflicts are plot-oriented and not actual character flaws. Trying to define a line where Luke can't be a Mary Sue, but Rey must be a Mary Sue is asinine and petty. They're both a leading protagonist in their respective films that serve a role to move the plot with their actions. Things like training and self-development are abridged because the audience, in a span of 90-120 minutes, are shown more of how amazing Main Protagonist is and why they are in that role.
Anakin was such a poor character in the Prequel Trilogy because his constant conflict was about being the "Chosen One." That he's so powerful, quick to learn, and capable of Force and practical skills that any mistake he could have made was eventually resolved by him being the "Chosen One." Unlike in The Clone Wars series were he makes mistakes, has to overcome both people and his own emotions. It doesn't even take multiple seasons as The Rako Hardeen arc does more with Anakin's character than three whole feature length films.