Luke Skywalker is the very definition of a Gary Stu (aka Mary Sue)
Mary Sue was a female character, written by a female fan, and it was such a sexist term that there was actually debate on whether or not a male character with the same traits would qualify for the same criticism!
It took time before the Gary/Marty Stu concept was even acknowledged. It's also originally a term regarding fan fiction, and no Force Awakens is not that. Rey is based on Kira, the female student Lucas developed for his sequels.
One thing about Rey is that her strongest detractors constantly lie about her and describe events in Force Awakens dishonestly in order to bash her (let's ignore the crappy Last Jedi because this started in TFA). They call her perfect even though she makes a series of mistakes in the movie:
-She screws up with the Rathars, almost killing Finn and Han and nearly getting the Falcon destroyed.
-She childishly wanders away from the group and gets herself captured by Kylo, which serves as an unnecessary distraction while trying to blow up Starkiller.
-She spends most of her saber fight against Kylo looking foolish, literally trying the same forward thrust over and over and over.
They also completely warp her fight against Kylo, leaving out:
1. That even Finn held his ground against Kylo;
2. That Kylo was horribly wounded by the same weapon that tossed a group of troopers;
3. That Kylo wanted to train her, not hurt her;
4. That only the Force allowed her to get the upper hand;
5. That she did not defeat Kylo;
6. That she fended for herself using a staff for years on Jakku, unlike farm boy Luke.
Now:
https://tvtropes.org/pmwiki/pmwiki.php/Main/MarySue
The primary definition of a Mary Sue:
"The prototypical Mary Sue is an original female character in a fanfic who obviously serves as an idealized version of the author mainly for the purpose of Wish Fulfillment."
LUKE's very name is based on George's last name, LUCAS. George has stated on his own that Luke racing around in his desert homeland of Tatooine is directly based on George growing up in Modesto racing old cars with his friends (also what American Graffiti is partly based on). Luke IS FACTUALLY an author avatar/insert.
"The canon protagonists are all overwhelmed with admiration for her beauty, wit, courage and other virtues, and are quick to adopt her as one of their True Companions, even characters who are usually antisocial and untrusting"
That last part describes Han Solo warming up to Luke and becoming his best buddy.
Also overwhelmed: Leia, who comforts Luke over the loss of Kenobi that he had known for a day... WHILE Leia ignores that her family and friends and people were destroyed in a planetary genocide!
LUKE'S FEELINGS ARE JUST TOO IMPORTANT! He sucks up all the attention and sympathy.
"the canon characters are quickly reduced to awestruck cheerleaders"
Leia's not done being overwhelmed. Even though she just met Luke, and no one has seen him fly anything, AND he's NEVER flown an X-Wing, he is tossed into one to fight for the Rebellion's very survival! Biggs (actual trained fighter pilot) didn't vouch for him, because he doesn't run into Biggs until the two are getting in their ships.
All Luke ever had to say was that he's "a pretty good pilot," and as a male, he's in the clear to do ANYTHING. Rey says she's a pilot, and some people just don't think that's good enough.
Basic double standard... oh but women can't drive, right? LOL!
"watching from the sidelines as Mary Sue outstrips them in their areas of expertise"
Vader: Fighting with a saber for longer than Luke was alive. Defeated countless Jedi as he lead the Jedi purge. Is considered one of the best lightsaber users EVER. Trained for many years to become what he is.
Farm Boy Luke: Never received lightsaber combat training, and in fact minimal Force training overall. Luke BEATS Vader on the SECOND lightsaber fight of Luke's ENTIRE LIFE! Becomes a Master with next to no training.
"She also lacks any realistic, or at least story-relevant, character flaws — either that or her "flaws" are obviously meant to be endearing."
Luke's flaws: Um, he's too nice? Too determined? Too pure and good!
Luke built a lightsaber yet never learned how.
Luke used a Force Pull at the opening of Empire Strikes Back even though he didn't even know telekinesis was possible using the Force, because it was never even shown in A New Hope! I GUESS LUKE INVENTED IT!
"She has some sort of especially close relationship to the author's favorite canon character"
Son of Darth Vader, brother of Princess Leia. These are the first two main characters we see in the entire franchise, so of course Luke is related to both of them! This is actually Lucas' own "fan fiction" of sorts, because he literally wrote A New Hope with Luke being unrelated to Leia and Vader. He changed Vader in ESB and he changed Leia in ROTJ (yes, Yoda's "there is another" was written to refer to another self-exiled Jedi who would come back).