feat: Add signup/signin with Google functionality features

[nikita-9112]

Problem Statement

we should implement Google OAuth 2.0 (Sign-In with Google)., allowing users to create an account or log in using their Google account. This improves user experience and reduces friction during registration.

Proposed Solution

• [Add Google Sign-In button on login and signup pages
• OAuth 2.0 flow implementation for secure authentication via Google
• ]Backend integration with Node/Express to handle Google auth tokens
• User session management (JWT) after successful Google signup/login
• Basic error handling and user feedback for auth failures
• Profile data (name, email, picture) store in MongoDB for new users

Example flow:

1. User clicks “Sign up with Google”.
2. Google OAuth popup opens, user consents.
3. Backend receives code/ token, validates with Google.
4. If user exists - login, if not - create new user - signup.
5. JWT returned and stored client-side.

I am highly interested in implementing this feature under Gssoc26. Please assign this issue to me.