Having such a deep emotional connection for people you just met is, quite frankly, unbelievable. She has no real reason to care about these people.
it's not about the length but the events that shape their perspectives and relationships, in fact, there are many and I mean many narratives that tackle friendship, relationships, self-reflection within a span of a day, to criticize it as being unbelievable just doesn't work, especially when the larger narrative as whole is not constraint to a set amount of time to tell it's themes, characters, and main plot. criticizing something for not abiding by our logic of reality is moot, as a fictional narrative has to be consistent with its own internal logic and not the logic of the actual world, and the film clearly shows us that it is consistent with its own internal logic.
And I don't see how other characters liking Rey as proof of their emotional connection. Everyone liking the protagonist is a classic defining trait to being a Mary Sue
this only applies if the protagonist has done literally nothing to earn their emotional connection or respect which is not the case in the context of Rey, this is reinforced by Finn and Han Solo.
Rey has no reason to be such a good person, she has no reason, as a likely starving person, to give up a large amount of food to some random robot, she has no reason to attack a man that the robot said stole its friend's jacket
yes, you can, especially when it's within the characters personality this acts as both a logical way for the protagonist to do the things she does as well as being a character flaw, it's called stubborn altruism, coupled with Gullibility.
And believability is one of the few imperative standards to character writing.
only to its own internal logic.
And her "emotional connection" is very debatable. She didn't care about the Resistance when she ran away into the forest
she avoided the call to action, that's what all monomyth characters do, it's the reluctant hero.
Luke Skywalker in a New Hope outright declines to save Princess Leia, it's only after his family is slaughtered that he takes the call to action, and Rey does the same when she pulls the saber from the snow.
just because they are reluctant does not mean they don't care.
Doing the right thing is the effect to an impactful cause. The desire to do the right thing should not be the cause that leads to the effect of doing said right thing.
Batman doesn't kill people because 'it is the right thing to do", he does it because he hates death and would never purposefully inflict it because he remembers the pain of the death of his parents.
No, lets look at the Joker in the Dark Knight, He does a ridiculous amount evil for absolutely no logical reason, this is one of the major themes of the film, it's constantly told to us in meta-narrative and within the context of the actual narrative of the film, Alfred makes a reference to this "Some People just want to watch the world bur".
now let's look at Joker's quotes to why he does what he does
Introduce a little anarchy. Upset the established order, and everything becomes chaos. I'm an agent of chaos. Oh, and you know the thing about chaos? It's fair!
this along with intentional contradictory comments makes the Joker's intentions actually blurry to the characters within the narrative.
it boils down to, He wants to create Chaos.
why does he want to create Chaos?
Because he finds it Fun
Why does he Find it Fun
Because His Insane.
His Insanity is one of his character traits that acts both as his motivator as well as his character flaw as he has multiple opportunities to kill Batman but chooses not to do so because it's "Fun" This applies to Rey with her altruism, the only difference between these two characters are their roles within the story.
If a character checks off every single thing in a list defining a trope, then it's safe to assume that the character falls into a trope.
The problem is that the standard your using to describe a Mary Sue is inaccurate
The effects that you talk about are because the character is a Mary Sue. The archetype has effects on the world, as every archetype does.
No, this is objectively inaccurate, it's when the author intentionally alters the internal logic, consistency, reality of the narrative and the characters personalities to glorify a specific character, this specific character becomes a Mary Sue, which is why Mary Sue is a trope and not an archetype, these two are vastly two different things.