"In a statement given to Reuters, Apple said that Wyden's letter gave them the opening they needed to share more details with the public about how governments monitored push notifications."
Just as an aside on metadata, I find it really frustrating that I can't just read the statement. There's a MacRumors article about a Reuters article about something Apple told them. I went to the Reuters article, but it still only contains one quote pulled from "a statement". I don't imagine Apple sent a major news organization an on-the-record statement with the restriction that they were only allowed to paraphrase it.
I run unified push on my Nextcloud server with app on device called Nextpush. This is used by some apps I use.
Some apps use web sockets, but I understand this is resource consumptive when constantly running in the background.
Some apps are able to piggy back on my Cheogram app for push notifications.
I use an Android fork without any Google Play Services. I don't know what is possible with Iphones.
I would assume that just prevents the display on your phone. Apps still send attempts at notifications through Apple servers I believe. This might work if you disable them in the app itself instead of your phone settings