Well, in this kind of fanfiction, one possibility is that the Gotei 13 members might be amazed by Ichigo's growth. They could see his new powers and techniques during the fight with Ulquiorra. Maybe they would start to respect him more as a true force to be reckoned with in the Soul Society.
This scenario in the fanfiction might lead to new alliances or rivalries. For instance, if Ichigo impresses certain members of the Gotei 13 during the fight, they could form an alliance later. Or, if Ulquiorra manages to outwit Ichigo while being watched, some in the Gotei 13 might see him as a more dangerous foe than they thought and target him more aggressively. Also, it could affect how Ichigo is perceived in the overall story. If he wins with great skill in front of the Gotei 13, his reputation could soar, and he could be more involved in Soul Society affairs.
Toge Inumaki is important too. His special cursed speech ability makes him stand out. Also, the principal of the school, Masamichi Yaga, is likely to be important as he is in a position of authority and has an influence on Gojo and the other students. There could be other characters like the members of different clans that also play roles in the complex web of the story.
It's hard to pinpoint exactly where Gojo is at any given time in the manga. His whereabouts change as the story progresses and different scenarios unfold. It could be in a supernatural realm, a mission site, or interacting with other characters.