Can you have push notifications on a web app that will be used by smartphone users?

I have a web app that will be used by iOS and android users on their browsers

Is it possible to have push notifications just like native apps would have?

Safari doesn’t support push, Chrome does. Other browsers: some do, some don’t.

In general push support for mobile browsers is not very mature yet. Best ask your push provider what they do or do not support. Ionic Push for example only supports push in native app environments as far as I know.