Expand Firebase page with setup, Auth, and database guides

[jesskuras]

Description of what this PR is changing or adding, and why:

Expands /data-and-backend/firebase with on-domain setup instructions, code examples, and architectural guidance for building Flutter apps with Firebase:

• Adds a summary table of common Firebase services for Flutter (cloud_firestore, firebase_data_connect, firebase_auth, firebase_storage, firebase_ai, cloud_functions / firebase_functions, and firebase_crashlytics).
• Adds a Connect a Flutter app to Firebase section walking through flutterfire_cli, flutterfire configure, and Firebase.initializeApp().
• Adds an Authenticate users with Firebase Authentication section with a StreamBuilder auth-state example and email/password sign-in.
• Adds a Store and sync NoSQL data with Cloud Firestore section showing how to write documents and stream realtime query snapshots.
• Adds a Query relational SQL data with Firebase SQL Connect section explaining generated type-safe Dart SDKs for PostgreSQL.
• Adds a Share Dart code with a serverless Firebase backend section highlighting Cloud Functions for Firebase in Dart and the shared-package pattern.
• Updates the Firebase for Flutter description in llms.txt.

Issues fixed by this PR (if any):

PRs or commits this PR depends on (if any):

Presubmit checklist

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• This PR follows the Google Developer Documentation Style Guidelines—for example, it doesn't use i.e. or e.g., and it avoids I and we (first-person pronouns).
• This PR uses semantic line breaks of 80 characters or fewer.

[flutter-website-bot]

Staged preview of the updated docs.flutter.dev site (updated for commit b1f0e4c):

https://flutter-docs-prod--docs-pr13980-expand-firebase-page-whwl6oj5.web.app