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.
Celebrating Years Season 2, episode 13 was the 13th episode of Celebrating Years Season 2. The play told the story of a young man with a mysterious background, Fan Xian. He had experienced the trials and tempering of his family, the martial world, and the court. He upheld justice and kindness and began a new journey in life. In this episode, the news of Fan Xian using the name of investigating corruption to target the Second Prince's faction spread like wildfire in the Jingdou officialdom. At the same time, the murderer of Baoyue Brothel was finally caught. The battle between Fan Xian and the Second Prince was becoming increasingly white-hot. Baoyue Brothel became a tool for the Second Prince to check and balance Fan Xian. The Second Prince tried to pull Fan Xian into the water and cause the people to boil. Fan Xian walked the path of being close to the people. What he valued more was the will of the people. Fan Xian asked his subordinate Deng Zi Yue to spread the word that the manager of Baoyue Brothel was Yuan Meng, and Yuan Meng was an old lover of the Second Prince's subordinate, Li Hongcheng. This was the reason why the Second Prince was framing Fan Xian. Fan Xian and the Second Prince displayed two countermeasures. Fan Xian walked the path of being close to the people. What he valued more was the will of the people. Therefore, Fan Xian asked Deng Zi Yue to spread the word that the manager of Baoyue Brothel was Yuan Meng, and Yuan Meng was an old lover of the Second Prince's subordinate, Li Hongcheng. Anyone with a brain would think that the Second Prince was framing Fan Xian. As for the details of the specific plot, one had to watch the 13th episode of the drama to understand.
The specific plot of the 131st episode of the second season of the celebration is not mentioned in the given search results, so I don't know what the plot of the 131st episode is.