first question is how old??
don’t try helping fix her, just try compassion and care. If she interrupts n ruins the class, that IS frustrating, but in your own mind, view her as someone who cannot control their behaviour or someone lacking social skills (even if it’s not) and respond as if she was- say good question, that you’ll think about it, please raise your hand next time, etc only with gentleness. If punishing a student doesn’t help or is counterproductive, you can be pretty sure there’s something more going on than leitzanus. Sounds like the principal knows this and thus treated the situation in a fitting way. S/he should follow up on making her apologize if he told her too perhaps, unless he thinks it might be detrimental. Ask him/her for advice, i.’m sure the principal knows her story better.
As an aside, for me, introducing a project would be a punishment, not reward! Try specific goals- not ‘behaving’, thats too general, but not calling out for half hour periods, or raising her hand when she wants to say something. Give her a point for every half hour she stays quiet/every time she raises her hand. And ask HER what she would like for the reward. If she’s not interested at all, it wont work anyhow. And keep it private! No one else should know anything about it