How to solve not receiving push notifications on your iPhone

There are two main causes of the problem of not receiving push notifications on the iPhone.

You have not granted permissions in the first place.
Low Power Mode is turned on.

Grant permissions

Tap Settings -> [App name], and you can check the permissions granted to the app.

Tap "Notifications" in the list and make sure it is turned on.

Many apps will display a modal when you first open the app after installation and ask for push notification permissions.

Do not turn on Low Power Mode

You may not receive push notifications when the iPhone's Low Power Mode is turned on.

Tap Settings -> Battery and turn off "Low Power Mode" if it is set on.

Low Power Mode can cause other problems besides push notifications, such as not receiving emails, so it is a good idea to check the Low Power Mode setting if you encounter any problems.