Another reason could be related to the overall political situation after the Kage Summit. If there were new alliances or tensions, and Sakura was somehow involved in a way that put Naruto in a difficult position, he might have decided to ignore her as a way to protect himself or his own goals.
One possible reason could be that something happened during the Kage Summit that made Naruto lose trust in Sakura. Maybe she made a decision or took an action that he didn't agree with. For example, if she sided with someone against Naruto's ideas regarding the situation at the Summit.
It might be that Naruto was deeply hurt by something Sakura said or did at the Kage Summit. Perhaps she made a comment about his abilities or his role in the events, which made him feel like she didn't have faith in him. So, in response, he chose to ignore her.
She could be confused at first. She might not understand why Naruto is suddenly ignoring her, since they were friends before. So she might try to approach him to ask what's wrong.
Another reason could be that Naruto is trying to protect Sakura in his own way. He might think that by ignoring her, he can keep her out of harm's way. If he senses that there are dangerous enemies lurking around, he could be trying to create a distance between them so that Sakura doesn't get caught up in any potential battles or threats.
It could be due to some sort of chakra imbalance caused by the intense events at the Summit.
In the fanfic, Naruto being cold after the Kage Summit could lead to some interesting character developments. His friends might be worried about him and this could strengthen their bonds. Also, it could be a sign of some sort of new power or curse that he got during the Summit, which would then drive the plot forward as they try to figure out what's wrong with him.
In some fanfics, Naruto may ignore Sakura because he has his own emotional traumas to deal with. He might find Sakura's presence a reminder of things he wants to forget or move past, so he chooses to keep his distance. For example, if he has faced a lot of rejection from her in the past, he could decide to just cut her out of his life.
A new, young ninja from a minor village could be the main character. They could be trying to make a name for themselves and their village at the Kage Summit. They might get involved in some political intrigue or even a fight between the Kages and prove their worth.
Perhaps in the fanfic, a young shinobi manages to infiltrate the Five Kage Summit and has a significant impact on the discussions. This shinobi could bring new ideas or warnings that change the course of the kages' decisions. For example, he might have uncovered a plot by a rogue ninja group to take advantage of the kages being gathered in one place. This would not only create tension between the kages and the external threat but also among the kages themselves as they debate how to handle this unexpected situation.
It could be Naruto himself. Since he has a connection to all the villages in some way, he could play a crucial role in the fanfic, perhaps as a mediator or someone who uncovers a hidden conspiracy during the summit.
In a 'Dark Naruto Kage Summit' fanfiction, it's possible that Dark Naruto is actually a misunderstood figure. He arrives at the summit not to cause destruction but to seek help. His dark transformation might be the result of an experiment gone wrong that he had no control over. The Kages, initially seeing him as a threat, might come to realize his true situation after he reveals his story. This could lead to a different kind of relationship between Naruto (even in his dark state) and the Kages, where they work together to find a solution to his problem.
Well, in the 'Naruto goes to the Kage Summit' fanfiction, Naruto could be in for a wild ride. He might be representing Konoha in some crucial discussions. There could be political intrigue among the Kages, and Naruto, being Naruto, would probably try to cut through all that and promote unity. He may also show off some new jutsu he has learned to gain the respect of the other Kages.