Honestly OP, I hear you. Some of your responses to people are quite blunt, but I get that it's coming from a place of just wanting to help your DD.
As for the app, yes, it was a mistake, but I get that you were only doing your best, trying to help you child fit in, supervising the chat, but still, this happens and you're upset. Perfectly rational.
You've gone to the school and aren't happy with their response because when it happens outside of school, there's very little they can do. Sure, maybe the chat and threats have felt like they may spill into school, a valid concern, but unless it's happened at school, the school is so very limited in what they can do. If they did something like suspend the child, then the school would have those parents all over them too, saying it's not the school's business. They really can't win here.
What I will tell you, is that while they can't say is out loud, schools do wish parents would involve the police a lot more regularly. It's the only way to get some families to sit up and take notice.
I know someone people will say the police have better things to do and while they're not wrong, nipping this sort of behaviour in the bud in Primary School could be really helpful long term for society as a whole.
I'm sorry this has happened and I'm sorry your daughter was upset, but kids who bully others are genuinely very, very sneaky and they're very good at hiding the parts that happen in schools. Call the police and a few teachers and probably some other families will be cheering you on.