It could strengthen his relationship with Hermione. Since Hermione is always interested in knowledge and research, when Harry has this vision, she would be eager to help him figure out what it means. They would spend more time together in the library, looking through old Divination books and other magical texts. This shared experience would bring them closer.
His relationship with Ron might be a bit more complicated. Ron might be a bit more skeptical about the vision at first. He could make jokes about it, thinking it's just another one of Divination's flaky predictions. This might cause some tension between them until the vision starts to prove itself. Then Ron would feel guilty for not believing Harry and would try to make it up to him, which would in turn strengthen their bond.
If Naruto gets a new bloodline, his relationship with Sasuke could become even more complex. Sasuke might be jealous of Naruto's new power, or it could be a reason for them to team up again to explore the origin of the bloodline. With Sakura, she might see Naruto in a new light, either being more attracted to his new strength or being worried about the potential risks of the bloodline.
In the fanfic, Harry's vision in Divination class could be about a future event involving one of his classmates. For example, he might see Neville getting into a dangerous situation with some magical plants in the greenhouse. Harry then decides to keep an eye on Neville and prevent the situation from happening. This could also lead to a sub - plot where Neville starts to suspect that Harry knows something about his future and there's some tension between them until Harry finally reveals what he saw in his vision and they work together to avoid the danger.
His friends usually find it quite amusing. Ron and Hermione might at first be a bit exasperated but then they end up enjoying the chaos. For example, when Harry pranks the Slytherins, Ron might be initially worried about getting in trouble but then laugh when they see the Slytherins' reactions. Hermione, on the other hand, might scold Harry but secretly be entertained.
The teachers would also be concerned. Dumbledore might try to have a deep conversation with Harry to understand his motives. Some teachers might see it as a sign of weakness or that they have failed in some way to make Hogwarts a comfortable place for Harry. As for his enemies, they might see it as an opportunity to strike while he's vulnerable.
His hatred might make him more distant from the other demigods who still have some respect or hope for Olympus. They may not understand his extreme feelings and this could create tension.
The black chakra could make other characters view Naruto with suspicion. His friends might be worried that this new power is corrupting him, which could strain their relationships. For instance, Sasuke might see it as a sign that Naruto is becoming more like the enemies they've fought.
There are quite a few fanfics where this happens. One popular one is 'The Mystic Visions of Harry' where his divination experiences lead to unexpected adventures.
With his friends like Sakura and Kakashi, they might be initially confused but then supportive. Sakura could be worried that Naruto is getting involved in something dangerous related to the moon, but also trust that he knows what he's doing. Kakashi, on the other hand, would likely be more intrigued and offer his wisdom and guidance as Naruto explores this new aspect of his life.
If Harry uses magic as a kid, it might make him more of an outcast among the non - magical Dursleys. They would be even more afraid and resentful of him. But with his friends at Hogwarts like Ron and Hermione, it could strengthen their bond as they are all fascinated by magic. They might look up to him more for his early magical abilities.
With the teachers, like Dumbledore, he might be treated differently. Dumbledore might see this transformation as an opportunity for Harry to learn new things about the wizarding world from a different perspective. And some of the more traditional teachers might have different expectations of Harry's behavior in class now that he is a girl.