I think most apps that people would be concerned about are using the ping to wake method, this vulnerability still affects them using metadata and traffic analysis. For example, can tell what app is receiving a wake and when, so they might know every time you get a message on signal even if they don’t know the contents.

There is a fork of Signal called Molly that supports websockets (persistent connections) or UnifiedPush, a push service you can self-host that uses it’s own client on the device. Of course those have to battle with battery optimization stuff in the OS.