It can make his relationships more strained. For example, he might push his friends away, thinking he's a burden to them. His teammates might not understand his behavior at first and become frustrated. But some might also be more determined to help him.
His depression could strain his relationships with his friends. They might not understand why he has become so withdrawn and moody. For instance, Sakura might try to reach out to him, but Naruto could push her away, causing a rift in their friendship.
With his wings, Naruto could have a different dynamic with his friends in Team 7. Sakura might be in awe of his new form and be more protective of him, fearing that his wings could make him a target. Kakashi, on the other hand, would see it as a new challenge for Naruto to master and would train him to use the wings effectively in combat and other situations.
In the fanfic, Naruto's struggle with depression would have a profound impact on his relationships. His friendship with Kakashi - sensei might be tested. Kakashi is used to Naruto's determination, but now he has to deal with a Naruto who is withdrawn. He might struggle to find the right way to encourage Naruto. Naruto's relationship with the villagers could also take a hit. They may not understand mental health issues and see his depression as something to be ashamed of. This could lead to Naruto feeling even more isolated from the community he once fought to protect, while his true friends' efforts to bridge the gap could become a central part of the story.
If Naruto has a physical disability like a broken arm that doesn't heal properly in fanfiction, his friends like Sasuke and Sakura would need to step in and help him more. Sasuke might be more protective, which could change their dynamic from a competitive one to a more collaborative one. Sakura could use her medical skills to try and find a way to heal him, which would bring them closer. His relationship with his teachers, like Kakashi, would also change as they'd have to adjust their training methods.
His relationship with Naruto would become more complicated. Naruto might be torn between believing in Sasuke's innocence and following the village's decision. Sakura would be deeply affected too. She might be in disbelief and try to find a way to get Sasuke reinstated.
In certain fanfictions, the izuku system is a secret. This secrecy can strain his relationships as he has to constantly lie or be evasive about his sudden improvements. But when the truth comes out, it can either lead to a huge rift or a deeper understanding among his friends, depending on how the writer chooses to portray it.
His relationship with his sensei, like Kakashi, could become more complex. Kakashi would feel guilty for not being able to protect Naruto from the experiments. And Naruto might start to question Kakashi's ability to keep him safe. This could lead to a strain in their relationship at first, but later they could grow closer as Kakashi helps Naruto recover from the trauma of the experiments.
With the other members of Young Justice, his injury could bring out their more nurturing sides. They might take turns looking after him, which could strengthen their bonds. On the other hand, some might see him as weakened and question his leadership abilities if he was in a leadership role before. For instance, Aqualad might have to step in more often to lead missions, causing some tension between them as Robin recovers.
Enemies would definitely be more cautious around Naruto. Those who once underestimated him would now fear his golden chakra. This could lead to some enemies trying to find weaknesses in it. Meanwhile, Naruto's new power might also attract the attention of mysterious characters who want to guide him in using it, which could cause some friction with his existing relationships as he has to decide who to trust.
His friends would be extremely worried. Sakura, for instance, would likely try to use her medical skills to help him and also try to figure out why he's doing it. She might be angry at first for him harming himself but then become very concerned. His relationship with Sasuke could also change. Sasuke might see Naruto's self - harm as a sign of weakness or, on the other hand, it could make him more empathetic towards Naruto as he has his own inner demons.