Advisable to have Apple Sign-in only happen on Apple devices/ iOS devices. Don't do Apple signin on Android. nevertheless.

If authentication is successful, You can consider setting up Deeplinks for your app. Such that redirects from Chrome to your web url will launch the mobile app and perform the required operations.

On Android Instead of opening up Chrome to perform the Sign-in operation. Consider opening the url in a dialog or new page that is a Webview. that way you can easily manage the redirects from within the Webview. Launching Chrome to perform an action and then redirect back to an App, is kind of an iOS behaviour.