The natural way to use Firebase on mobile is using Android or iOS.
However, I'm in this situation where a client who developed a web app wants to receive push notifications when:
Is that possible?
Note: According to Firebase Documentation, client web apps can receive push notifications when they are in background, but I'm not sure if that extends to web apps running on a mobile browser in background.
Yes, you can receive push notifications on your mobile even when your browser is not open, but you need to enable it by pressing Allow when prompted, as below.