How to implement Login with Apple in WebView application?

Question

JSON Web Token

There is a WebView application.
Implemented an entrance in it through AppleId according to the instructions on the website of the developers Incorporating Sign in with Apple into Other Platforms.
From a PC and Android, the input works, but not from the iPhone - when a fingerprint is recognized, it simply reloads the page.
Do I need to write a separate authorization script for the iPhone? Or is it possible to add this somehow?