When Anon goes to confront Soyo at her home, just before the climax of episode ten, it’s the first time that Anon has the upper hand over her and can see her as human, somebody she can relate to.
To Anon, Soyo had always been the sort of person she wanted to be: smart, elegant, kind, calm. The sort of person who can drink Earl Grey tea without sugar, who’s kind and friendly with everybody. Throughout the early episodes you can see how impressed Anon is with her. She never saw through the facade Soyo put up (neither did Tomori or Taki to be fair). Even when Soyo became angry in episode 7 for them having played haruhikage, (Crychic’s song), Anon took it as another example of Soyo’s kindness, her being angry out of concern for the feelings of Sakiko, Crychic’s ex-leader, who was at the concert. She had to hear from Taki of all people that Soyo had used her, that Soyo had never been serious about their new band, saw her only as a tool to reunite Crychic.
Anon being Anon her first instinct was not to be angry about it, but to see it as confirmation of all her worst self loathing. She isn’t needed, she isn’t special, she cannot even fool people that she is. Tomori starting doing solo concerts is a confirmation of this to her, as she completely misunderstands what she’s trying to do. Like with her attempt to study abroad, she wants to give up because it has become too difficult. Because Anon knows she only did it for ulterior motives, to look good in class, to become popular: she was using Tomori as much as Soyo was using her. It’;s only after Tomori literally chases after her and tells her she needs her, shows her that regardless, Anon still struggled for the band, that she relents.
She may have had awful, selfish motives but Tomori still accepts her. And because of that she now has the courage and clarity to recognise that she and Soyo are the same, that Soyo is not some paragon to emulate, but as human and flawed as herself, which means Anon can now play her like a fiddle. Being so similar she knows exactly which buttons to push to get Soyo to come to the next performance and once she does, getting her onstage is easy. Against the combination of Tomori’s earnestness and Anon’s maliciousness Soyo never stood a chance.
And because Anon can no longer put her on a pedestal, does finally see her as a human being, she’s now able to treat Soyo as she does the other members, as a friend she can give a nickname to, whether it’s appreciated or not. As with Taki (sorry, rikki) she shows her love through teasing. She still seeks her approval but now from a level playing field, just like she does with Taki.