You cannot handle a TOS violation for another streamer.
There is nothing you can do to help this streamer. As the streamer appears to have broken the rules of Twitch.
It’s not your problem TOS/banning to fix, and this forum cannot help you with that.
But you can go and add additional filters/rules and so on to your bot to prevent it happening again to other streamers.
This won’t help with what has occured.
Edit: I misread I thought the STREAMER got banned. (or it’s unclear from your message, whom got banned)
It was your bot that got banned. You’ll just have to wati for Twitch to get back to your via the support channels. And being a “tagged bot” won’t help your account get banned if it’s deemed to be breaking the rules/TOS
Additionally the streamer themself shouldn’t be declaring they are underage since they themsleves could get banned