He might become very withdrawn. Bell could start to isolate himself from others, especially those associated with Hestia. He may no longer trust as easily as he did before.
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.
The gods would have a variety of reactions. Some might see it as a sign of something special, perhaps a new era beginning. Others might be more cynical and think it will bring trouble. For example, Freya might be interested in the child's potential and keep a close eye on the family. Zeus, if he were still around, might offer his wisdom on raising a child with such unique parentage. And Hermes could spread the news far and wide among the gods and mortals alike.
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.