What if there was an open source software one could setup on a server that would provide push services for all these apps and would interact with one open source client running on android.
That way one would have the energy saving benefits of only handling one server connection, but the privacy benefits of a private server for oneself/friends/people one trusts.
This is definitely not easy and would require coordination between many open source projects and also additions in Android to run on a system level (maybe in lineageos and similar), but I really think it would be worth it.