For android, Google uses Firebase Cloud Messaging, basically a server that pings the phone when a notification for an app is available, which wakes the app up to receive the notification. There are alternatives but they need to be adopted by app devs for them to work.

For people running a degoogled android, they’ll notice most apps won’t receive any notifications until they open the apps since most apps rely on Google Play Services to receive a ping from FCM.

I don’t have any google play services so most of my apps don’t give me push notifications but I do have WhatsApp installed and that still receives notifications, they’re sometimes delayed by a few minutes which makes me think Meta have their own implementation/alternative to FCM but I’m not sure.

For Signal, their servers tell Googles FCM servers that you have notifications waiting on Signals servers and to wake up your Signal app so it can communicate with Signals servers to receive your messages.

WhatsApp and Signal claim/have end-end encryption on their messages but that shouldn’t matter when specifically looking at Googles FCM servers so, at most it would be meta data that could be obtained from the FCM servers.

jami.net/unifiedpush/ has a pretty basic explanation of push notifications on android and also showcases an alternative to FCM unifiedpush.org which has a nice little diagram about push notifications on android. Unfortunately, Unifiedpush is not widely adopted by many applications.

So there are ways to avoid Googles FCM servers on android using Unifiedpush or always having the application on in the background but for the most part FCM is used.