Android
Turn On or Off Screen Wake for Notifications auf Android
When the display stays black after a notification arrives, the phone is not broken. Android simply has the wake-on-notification option turned off, so the lock screen never lights up unless you press the power button yourself.
This behavior is controlled from the lock screen settings, separate from Always On Display and separate from the notification permissions of individual apps. Even with alerts fully enabled for an app, the screen can stay off if this toggle is disabled.
To change it, go to Settings ➔ Display ➔ Lock screen ➔ Wake screen for notifications. Enable it to have the screen briefly light up on incoming alerts, or disable it to keep the display dark and save battery.
Turning this on helps when you frequently miss messages while the phone sits idle. Turning it off makes sense if the phone is on a nightstand or desk and unwanted light or repeated wake-ups are the bigger annoyance.
Keep in mind that some manufacturer skins rename or relocate this toggle slightly, so if the exact label differs, look for wording tied to lock screen notifications rather than Always On Display.