> How do push notifications and similar things work on GraphenOS?

Some apps require Google's FCM for push notifications. You need to install Sandboxed Google Play services from the GrapheneOS App Store and grant them unrestricted battery access (so they can run in the background, which is required for maintaining a network connection to FCM and delivering notifications). https://grapheneos.org/faq#notifications

Other apps like Signal use their own background connections, for example WebSockets, to deliver push notifications, but keeping a connection open for each app consumes more battery life than just having one background network connection. Also, not every app supports this.

For Signal specifically, the GrapheneOS project recommends either using FCM via Sandboxed Google Play, or installing Molly (https://molly.im/), a fork of the Signal client for Android, which makes some changes to reduce battery consumption when using WebSocket-based notifications. It also allows you to use UnifiedPush (https://unifiedpush.org/) for notifications instead, but that requires an application called mollysocket (https://github.com/mollyim/mollysocket) running on a server.

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