Perhaps there's a plot against Harry by some dark forces, and the Potters believe that only they can protect him properly. They might think that the people who have been taking care of Harry so far are not equipped to handle the new and more dangerous threats. Also, it could be that the afterlife in the wizarding world has some rules or opportunities that allow them to try and get Harry back into their family fold. They could have been given a second chance, so to speak, and are eager to take it.
At first, it might be really awkward. Harry has grown up without them, so he may be hesitant and distrustful. But as time goes on, they start to bond over shared interests or magical abilities. For example, the Potters might teach Harry some family spells that he never knew before.
One possible motive could be that the Potters discovered some dark plot by the Malfoys involving Harry. Maybe they found out that the Malfoys were planning to indoctrinate Harry into their pure - blood supremacist ideology against his will. So, to protect Harry from that, they kidnapped him.
Yes, they might. Just like any other group of people, those who identify as Blacks or are part of the Potter family name (if we assume there are real people with that name) could be fans of the Harry Potter series and thus read fanfiction. Fanfiction offers a wide range of interpretations and extensions of the original story, and anyone with an interest in the magical world of Harry Potter could be drawn to it.
Sirius Black could also be part of it. He was Harry's godfather. He might have escaped from Azkaban earlier in this fanfic. He teams up with the Potters to rescue Harry. He could be the one who scouts out the Dursleys' house before the actual rescue operation, using his skills as an Animagus to stay hidden.
It could also be that the Potters are under some sort of magical influence or curse. In the fan fiction world, there could be a dark force at play that makes them see the twins as more important. This force might be manipulating their emotions and perception, leading to the neglect of Harry.
One possible reason could be that the twins might have some special abilities or circumstances that draw the Potters' attention more. Maybe they are more outgoing and seem to need more immediate care or guidance. Another reason could be that there is some sort of miscommunication or misunderstanding within the family. For example, the Potters might think Harry is more self - sufficient when in fact he also needs their love and attention.
Harry might become withdrawn and introverted. Feeling unloved and unwanted, he could start to keep to himself more, spending time alone in his room or exploring the grounds of their home alone, trying to make sense of why his parents seem to favor the twins.
Well, he could discover new relationships his parents had. Maybe his mother Lily had a close friendship with a character we don't know much about in the official story. Fanfiction often delves into uncharted territories of a character's life. So, Harry could find out about the Potters' early days at Hogwarts, like their first encounters with certain teachers or how they formed their own group of friends.
He might become withdrawn. Feeling unloved and ignored, Harry could start to keep to himself more, not sharing his thoughts and feelings with his family. He may also become resentful towards the twins, seeing them as the cause of his being neglected, even if it's not entirely their fault.