How can I update to the iOS 13 public release?

You have to erase your phone and restore from the iTunes-based iOS 12 backup you made before installing the beta, and then update from there.

You can also erase your phone and set it up as a new device, but that will literally result in a phone with none of your settings set.

The best option for you is to delete your beta profile and wait for 13.1 and update to that when it's released on the 24th.

I was waiting for the 13 iOS but my phone is no updated when it already came out but the update didn’t show up.

Are you on beta software? If you aren't, your issue has nothing to do with what this thread is about.