Their relationship might also become more distant. Different sensei would mean different training schedules and different goals. Sakura could be spending most of her time in the hospital learning medical ninjutsu, while Naruto is out in the field training combat skills. They might not have as much time to interact and bond as they did in the original story.
If they had different sensei, their relationship could become more competitive. For example, if Sakura's sensei focused on making her a top - tier medical ninja quickly and Naruto's sensei was pushing him to master new powerful jutsu, they might compete to prove who is more valuable to the village.
One possibility could be that Sakura is under Tsunade's tutelage while Naruto is trained by Jiraiya. This would lead to different styles of training. Sakura would focus more on medical ninjutsu and precise chakra control like Tsunade. Naruto, with Jiraiya, would learn more about summoning jutsu and unpredictable combat styles. Their growth paths would diverge in interesting ways, affecting how they interact with each other and their roles in the village.
Their relationship could start off rocky as Kurenai might be hesitant to accept Naruto as her sensei. After all, Naruto is younger and has a very different style. But as time goes on, she would start to see the value in his teachings.
I think Orochimaru would be the most unexpected sensei. Usually, he's seen as a villain, but in a fanfiction, if he were to train Naruto, it would be extremely unexpected. He has a vast knowledge of jutsu, especially forbidden ones. He could teach Naruto some very powerful and unique abilities, but at the same time, Naruto would have to deal with Orochimaru's morally ambiguous nature.
If Sakura's genjutsu goes right, it could bring Naruto and Sakura closer. For example, if she uses a genjutsu to show Naruto a future where they are together and happy, it might make Naruto more aware of his feelings for her.
At first, Naruto might be a bit wary of Itachi because of his reputation. But as Itachi starts to teach him, Naruto would see his kind heart and wisdom. Their relationship could develop into a deep mutual respect. Itachi would see Naruto's potential to change the ninja world for the better, and Naruto would come to understand Itachi's sacrifices. They might start as teacher - student, but eventually become like family, with Naruto looking up to Itachi as a mentor and a friend.
Their relationship could start off as a typical student - teacher dynamic, with Naruto being the knowledgeable sensei and Anko the eager student. But as time goes on, they could become friends, sharing their past experiences and fears. Naruto could help Anko overcome her insecurities related to Orochimaru.
Naruto could use his own life story as a teaching tool. He could tell his students about how he was an outcast as a kid because of the Nine - Tails inside him, and how he overcame all the difficulties. This would inspire his students to keep going no matter what obstacles they face. He would also be very passionate about teaching them new jutsu and would probably show them some of his own unique techniques like the Rasengan.
Their relationship would be very strong. Jiraiya would see Naruto as not just a student, but also as a connection to Minato. He would be strict but also very affectionate. Naruto would look up to Jiraiya as a father figure, since he never really had one. They would share many adventures together, with Jiraiya teaching Naruto about life, love, and ninjutsu.
His friends might be a bit jealous at first. After all, Naruto is suddenly so interested in the Raikage. But they would also be supportive as they know Naruto is always looking to grow stronger. For example, Sasuke might be initially suspicious but then see the potential in Naruto learning from the Raikage.
The Naruto universe would be in for some chaos. Gaara's new obsession could disrupt the balance of power dynamics. If he starts to prioritize the fanfiction - related ideas about Sakura over his duties in the Sand Village, it could lead to political unrest or at least some tension between the Sand and Konoha. After all, his actions as a leader are important for maintaining peace between the villages.