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.
Maybe it has the ability to absorb chakra. So when Naruto is in a fight against an opponent with a large amount of chakra, he can use the sword to drain some of that chakra, weakening the enemy while strengthening himself. The sword could then store that chakra for later use, like to boost Naruto's own attacks.
It could be a sword that can cut through any substance, like the Susanoo easily. Just imagine Naruto swinging it and slicing through powerful jutsu defenses as if they were paper.