Implement Google OAuth Integration

[singhaditya21]

Implemented a complete Google OAuth 2.0 Authorization Code flow for the web demo application.
This replaces the previous simulation with actual integration logic.

Key changes:

1. Frontend (web-demo):

   • Added Google Identity Services script to index.html.
   • Updated app.js to initialize google.accounts.oauth2.initCodeClient and handle the sign-in flow.
   • Updated api.js to add googleLogin method which calls the backend, bypassing mock data.

2. Backend (backend/api):

   • Added GOOGLE_CLIENT_ID and GOOGLE_CLIENT_SECRET to config.py.
   • Updated UserCreate schema to support web platform.
   • Added GoogleLoginRequest schema.
   • Implemented POST /api/auth/google endpoint which:
     • Exchanges authorization code for tokens using httpx.
     • Retrieves user info from Google.
     • Finds or creates a user in the database.
     • Returns a JWT access token.

Verification:

• Verified backend endpoint logic using a Python script (verify_auth.py) that mocked Google API responses and database interactions.
• Verified frontend integration using a Playwright script (verify_frontend.py) that confirmed the Google Sign-In button triggers the flow and UI updates correctly.

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PR created automatically by Jules for task 5668877588095846487 started by @singhaditya21

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[singhaditya21]

Closing as a duplicate of #41, which implements the same Google OAuth flow and additionally merges cleanly. Consolidating on #41.