The Bleach anime mostly covers the manga, but there are some differences. Some filler episodes were added to extend the runtime, and certain storylines might have been condensed or slightly modified for better pacing in the anime.
Ichigo might gain new perspectives on his own power. If the fanfiction shows him in situations where he has to overcome even greater challenges, he could start to think about his own limits differently and maybe strive to be even stronger.
The story would become much darker. His friends would have to find new ways to protect the world without him. Rukia, for instance, might have to step up and take on a leadership role she wasn't fully prepared for. The balance between the Soul Society and the Hollows could be severely disrupted.
Ichigo might become more cautious. Usually he's quite impulsive, but seeing the future could make him think twice before acting. He doesn't want to mess things up more than they already might be in the future he saw.
Naruto's ability to use the Nine - Tails' chakra could turn into something like having a powerful spiritual beast companion in the Bleach world. Hinata's Byakugan could be enhanced to see spiritual auras more clearly and detect hidden spiritual threats. Their powers would also be influenced by the fact that they are now in a world with Shinigami, Hollows, and Quincy. They might learn new techniques from the Bleach characters and combine them with their own unique abilities.
If we think about the relationships in a Bleach and Highschool DxD crossover. The devils in Highschool DxD are used to a certain hierarchy and power play. When they meet the Soul Reapers, who also have a strict hierarchy, there could be clashes. For instance, Rias and Byakuya might initially have a tense relationship. Rias is used to being in charge in her own way, and Byakuya is a proud captain. But as they see each other's sense of justice and the need to protect their respective worlds, they could start to work together. And for the students in Highschool DxD, they might look up to the more experienced Soul Reapers. The Soul Reapers, in turn, might be amused by the more carefree and hormonal nature of the Highschool DxD students. This could lead to a mentoring - like relationship in some cases.
Their relationship could lead to a new era of cooperation between humans and Shinigami. Since Ichigo is a human with Shinigami powers and Yoruichi is a powerful Shinigami herself, their union might inspire more understanding and collaboration. For example, the Urahara Shop could become a more important hub for this new cooperation, with Ichigo and Yoruichi at the center of it.