Which system are you saying won’t pass the doorbell information to the phone App? On both Dahua and Hikvision P2P the doorbell is added by itself, whether it’s powered and addressed by the NVR or a PoE switch or an injector.
The NVR NATs the camera, doorbell or anything else powered off it to its own IP address and the camera or doorbell is still visible in the App. You can see the doorbell twice in the App, once as the doorbell and once as a camera on the NVR. It’s the doorbell that ‘rings’, not the NVR, the NVR just passes the information through from the SIP server on the doorbell.
The doorbell does need to be added to the App separately, or it won’t ring, which may be part of the confusion, but it works just fine. Certainly on the ones we’re currently installing.
If you think about what you’ve typed, you can access the individHal settings on each camera when connected from the NVR, but you have to go through the App on your phone or the NVR dashboard and because of the way P2P connects you to the cameras, it will quite happily let you log into the camera directly. It’s one of the great vulnerabilities of P2P as a means of accessing anything.