docs(auth, google): forward-port google-signin example to v13+ APIs (#8092)

* fix: social auth Google sign in result
- Google sign in result type in the latest version of @react-native-google-signin/google-signin has changed
* make example code work with old or new API
* lint: result of `yarn lint:markdown --write`

---------

Co-authored-by: Mike Hardy <[email protected]>

Author: tolypash

docs/auth/social-auth.md

@@ -312,10 +312,20 @@ async function onGoogleButtonPress() {
   // Check if your device supports Google Play
   await GoogleSignin.hasPlayServices({ showPlayServicesUpdateDialog: true });
   // Get the users ID token
-  const { idToken } = await GoogleSignin.signIn();
+  const signInResult = await GoogleSignin.signIn();
+
+  // Try the new style of google-sign in result, from v13+ of that module
+  idToken = signInResult.data?.idToken;
+  if (!idToken) {
+    // if you are using older versions of google-signin, try old style result
+    idToken = signInResult.idToken;
+  }
+  if (!idToken) {
+    throw new Error('No ID token found');
+  }
 
   // Create a Google credential with the token
-  const googleCredential = auth.GoogleAuthProvider.credential(idToken);
+  const googleCredential = auth.GoogleAuthProvider.credential(signInResult.data.token);
 
   // Sign-in the user with the credential
   return auth().signInWithCredential(googleCredential);