docs(auth): document free Credential Manager Google Sign-In via react-native

[rutvik24]

Summary

• Documents react-native-nitro-google-signin as a free (MIT) way to use Google’s latest Android Credential Manager Sign in with Google flow with React Native Firebase, including full Firebase signInWithCredential / linkWithCredential examples.
• Clarifies that @react-native-google-signin/google-signin only gets Credential Manager through the paid Universal Sign-In tier; the free public GoogleSignin API still uses the legacy Android SDK (deprecated, no Credential Manager).
• Adds a comparison table, Expo guidance (development build + Expo config plugin), and a cross-link from auth usage docs for revokeAccess().

Why

Google recommends Credential Manager for Sign in with Google on Android. Many RN Firebase apps already use @react-native-google-signin/google-signin; upgrading to Universal Sign-In for Credential Manager requires a paid license. react-native-nitro-google-signin offers the same modern One Tap–style flow on Android (and iOS) at no cost, with Expo support via config plugin—this PR makes that path discoverable in official RN Firebase docs.

Test plan

• Review rendered docs on social-auth Google section (comparison table, nitro install/sign-in/link examples, existing google-signin section unchanged in spirit).
• Verify links: nitro npm/docs, Credential Manager Android guide, Universal Sign-In pricing, Expo dev build + config plugin.
• Confirm docs/auth/usage/index.mdx revokeAccess note reads correctly next to existing Google Sign-In link.

[CLAassistant]

All committers have signed the CLA.

[gemini-code-assist]

Summary of Changes

Hello, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request enhances the documentation for Google Sign-In within the project. It provides developers with a clear, free path to implementing Android Credential Manager by documenting the use of the react-native-nitro-google-signin library. It also clarifies the distinction between the free and paid tiers of the existing Google Sign-In library, ensuring users can make informed decisions regarding their authentication implementation.

Highlights

• Documentation of react-native-nitro-google-signin: Added comprehensive documentation for using react-native-nitro-google-signin as a free, MIT-licensed alternative for Android Credential Manager support.
• Comparison Table: Introduced a comparison table in the social-auth documentation to clarify the cost and features of different Google Sign-In libraries, specifically highlighting the paid nature of Credential Manager in the standard library.
• Updated Revoke Access Guidance: Updated the usage documentation to provide generic guidance on using revokeAccess() across different Google sign-in libraries.

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[gemini-code-assist]

Code Review

This pull request updates the Google Sign-In documentation to introduce react-native-nitro-google-signin as a free alternative supporting Android's Credential Manager, alongside @react-native-google-signin/google-signin. Feedback on the code examples highlights potential runtime errors, specifically recommending the use of optional chaining when accessing response.data and verifying that getAuth().currentUser is not null before calling linkWithCredential.

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