Question:
Android - Show full-screen notification when app is in the background
Based on the documentation for setFullScreenIntent
(https://developer.android.com/reference/android/app/Notification.Builder#setFullScreenIntent(android.app.PendingIntent,%20boolean)), full-screen intents are intended for urgent, high-priority notifications such as incoming calls or alarms.
From the related article (https://source.android.com/docs/core/permissions/fsi-limits), there are guidelines on how to use this feature and limitations on its behavior, but the exact behavior can depend on the state of the device (locked /unlocked ...) and system-level restrictions.
These are untested notes based on research. While this answer is late for the original poster, I hope it is useful to anyone who encounters this issue in the future.