It doesn't. The API for displaying a notification is purely local.

Receiving a ping from Firebase Cloud Messaging triggers the app to whatever it does in order to display its notification. In the case of Signal, that probably means something like fetching the user's latest messages from the server, then deciding what to show in the notification based on the user's settings, metadata, and message content.

Here's example code for using FCM to show a notification. In this case, the notification content also passes through FCM, but Signal does not do that. https://www.geeksforgeeks.org/android/how-to-push-notificati...