It could also affect Hermione's relationships with her friends at Hogwarts. They might be a bit wary of her cousin from Durmstrang, especially if there are rumors or prejudices about the school. On the other hand, Hermione could use this as an opportunity to break down those barriers and promote better understanding between the two student bodies.
Hermione could start to compare the two schools more. Maybe she'll notice that Durmstrang has a more competitive environment, which could make her appreciate the more collaborative nature of Hogwarts. Or she might see that Durmstrang has some advanced magical techniques in certain areas that Hogwarts lacks, and this could change her view on what a 'good' magical school should be.
One possible plot could be Hermione feeling out of place at Hogwarts due to some unforeseen circumstances. Maybe she has a falling out with some of her friends or feels that the Hogwarts curriculum isn't challenging enough. So she decides to transfer to Durmstrang. At Durmstrang, she might face a lot of prejudice as she's a Muggle - born witch. But she could also make new friends and discover new magical techniques that are different from what she learned at Hogwarts.
One common theme is family secrets. Often, the discovery of the cousin leads to uncovering secrets about their family's magical heritage.
Well, one possible plot could be that Harry goes to Durmstrang to learn different kinds of magic not taught at Hogwarts. Maybe he discovers a new form of defensive magic there. He could also make new friends who have different views on magic compared to his Hogwarts pals. And perhaps he gets involved in a mystery that is unique to Durmstrang, like an ancient curse on the school or a hidden artifact.
Her relationship with Ron and Harry would be strained at first. They'd feel betrayed that she left Hogwarts. But over time, they might come to understand her reasons. At Durmstrang, she'd have to build new friendships. She might befriend some students who are more interested in academic pursuits like her. Her relationship with the professors at Durmstrang would also be different. Some might be more strict and traditional, while others might see her potential and encourage her studies.
One possible plot could be Hermione being selected for an exchange program to Durmstrang. There, she might face challenges in adjusting to their different teaching methods which are more focused on the Dark Arts in a controlled way compared to Hogwarts. She could also encounter new friendships and rivalries. For example, she might become friends with some students who are secretly opposed to the more extreme elements in Durmstrang's curriculum.
If Naruto had the Byakugan in a fanfic, it could completely change the power dynamics. He would have enhanced vision abilities like seeing the chakra points clearly. This might make his combat strategy more diverse as he could anticipate enemy moves better. Also, his training might take a different route as he'd need to master the Byakugan's unique skills on top of his already existing Uzumaki powers.
One of her friends could be a girl who is also interested in Muggle Studies, which is not really a popular subject in Durmstrang. They meet in the library while looking for books on the topic and start sharing their views on the Muggle world and magic. Also, there might be a young wizard who is against the more aggressive and dark - leaning teachings of Durmstrang and sees Hermione as an ally in changing the school's culture.
One implication could be a change in his relationships. His friends might be shocked or even turn against him as Jashinism is often associated with dark and violent practices. Naruto's moral compass would also be severely tested as Jashinist beliefs are not in line with the values he was brought up with in the original story.
Well, in this fanfic, perhaps Harry struggles with the more strict and traditional rules of Durmstrang. He could be constantly compared to Viktor Krum, who might be a year or two above him. This could create some tension and rivalry. Also, he might discover some secrets about Durmstrang's past that are linked to the Dark Arts, and he has to decide whether to keep them or expose them.