[Content Note: consent issues, murder/suicide analogies, spoilers for the ending of Passengers]
I think the movie does explain why she forgives him, but it isn't overly explicit about it, and a lot of it goes by really fast during the final extended action sequence, so it's easy to miss. The short version is that I see her becoming able to forgive him by first confronting the darkness within herself, her own fear and desperation, which allows her to empathize with what he did.
Some of this has been mentioned by others here, but I'll note that I need to discuss details of the ending, so SPOILERS AHEAD:
I think the first key moment is when Gus likens what Jim did to the actions of a drowning man. That's a bit dismissive of Jim's responsibility, which was more premeditated action than the reflexive actions of someone drowning, but the scene is followed shortly thereafter by Aurora experiencing her own near-drowning experience when the gravity generator fails. That experience makes the metaphor real for her, letting her feel desperation in a very visceral way, which has to affect how she thinks about his actions going forward.
Next there's the extended scene in the engine room, where they have to work together to save the ship, and where he ultimately is willing to sacrifice himself to save her and the rest of the passengers. That forces her to confront the prospect of being left alone on the ship as he was, and it's clear that the possibility terrifies her, as she works to bring him back. She has to confront her own feelings of fear and loneliness, even though she does it quickly without letting them paralyze her.
And then, finally, he is able to offer her meaningful restitution for the choice he took from her. He has found a way to put her, and only her, back into hibernation for the rest of the voyage, and he offers to do it. By then, having confronted her own fear, desperation, and loneliness, she can fully understand what the offer will cost him. But he has restored the choice and the agency that he took from her, so that her final decision is a truly free choice.
We don't know how long it takes for her to make that final decision. There's an indefinite time skip between the scene where he makes the offer, and the next scene at the bar. But I think that we don't need to fall back on Stockholm syndrome to explain why she chooses to reattach. She was already falling in love with him before she discovered his betrayal. By confronting the darkness within herself, she has become capable of empathizing with his situation, and truly forgiving what he did. And he has now twice demonstrated that he can act unselfishly for her benefit, in contrast to the selfishness that led him to take away her choice in the first place. In restoring her choice, he makes it possible for her to consider loving him again.
Another thought about the ending of Passengers: think for a moment about how selfish and shallow Aurora’s initial goal for the trip was. If she legitimately analogizes what Jim did to a kind of murder, then what she had planned for herself was a kind of double suicide, where she would twice become dead to everyone who had ever known and loved her, all for the sake of the book she planned to write about the experience. Those friends who recorded the farewell greeting to her will be dead and gone long before the ship makes landfall, never having heard from her again. Then she plans to do it again to her new society, counting on her money and the notoriety from her book to allow her to reintegrate into a future New York where no one who hasn’t read her book has any idea who she is.
In restoring her choice to her, what Jim makes possible is a different kind of life to write about, and a far more compelling book about experiences no one else will ever have, the back story behind the founding of a new society, and life with the guy who gave her the stars. As a bonus, there’s a chance that her friends back in New York will get to read the opening chapters before they die, and learn what she has made of her life.
Instead of a dilettante’s book aimed at would-be dilettantes, she’ll be writing the origin story for everyone in the new colony, about the people to whom they all owe their lives and future existence. Is it really so difficult to believe that the Aurora who has grown through the latter part of the movie might make that choice?