The problems were the methods I was trying to install the app on xbox. Searching for the app in the store on trying "install from my devices" from the store app in the pc wont work for a private group app.
Directed by support, I went on and opened the link that appears in the product identity section in the edge browser on the xbox and that worked.
https://www.microsoft.com/store/r/[APP STORE ID]
Thanks.