In fanfiction, Jiraiya seeing Naruto as Hokage can be a very emotional moment. It could be a vision Jiraiya has in a story where he's still alive, or perhaps it's a memory in a story set after his death. This often shows Jiraiya's pride in Naruto and his belief in Naruto's potential to lead the village.
It could be Kakashi. Even though in the original story he doesn't teach Naruto the Rasengan, in a fanfic he might have some hidden knowledge about the technique. Maybe he was secretly studying it himself and saw Naruto's eagerness to learn new jutsu, so he decided to share his knowledge and help Naruto learn the Rasengan earlier.
Seeing Naruto's power in fanfiction can greatly influence Boruto's character. It could make him more determined to reach his father's level. He might start training harder and be more serious about his ninja duties.
Boruto might be in awe. He has always known his father as the Hokage, a powerful and respected figure. Seeing Naruto's past full of struggles, loneliness, and determination would make him realize how far his father has come. It could also make Boruto more empathetic towards Naruto and perhaps inspire him to be more like his father in some ways.
Maybe in the fanfiction, Jiraiya is summoned by a new jutsu gone wrong. When he meets Boruto, he mistakes him for Naruto at first. As they interact, Jiraiya realizes Boruto's own unique struggles. He shares his wisdom about handling the expectations that come with being a ninja from a famous family, and Boruto learns a great deal from him.
In this fanfiction, Boruto might learn some unique ninja techniques from Jiraiya. Jiraiya could see the potential in Boruto and train him in his own unorthodox ways. Maybe Boruto would be introduced to Jiraiya's toad summoning, which could add a whole new dimension to his combat abilities.
It could also be that Naruto sees in Boruto's eye a sign of an emerging danger. The eye might hold a clue to a new enemy or a brewing conflict. Naruto, being the experienced ninja he is, would then start to take precautions and train Boruto more intensively to face whatever this sign in his eye indicates.
Perhaps an old enemy of Jiraiya who was thought to be defeated but has now resurfaced. This antagonist targets Boruto to get to Jiraiya, thinking that by harming Boruto, he can draw Jiraiya out and finally get his revenge. He would be a powerful and cunning foe, making it difficult for Jiraiya and Boruto to face him.