feat: implement Google OAuth 2.0 sign-in #1145

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Related Issue

Closes #ISSUE_NUMBER

Summary

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Changes Made

• Bullet list of implemented changes.
• ...

Testing

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Screenshots

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Checklist

• Code follows project style
• Tested locally
• No unrelated changes included
• Documentation updated (if applicable)

Resolves #1145

Description

This PR resolves the requested feature by implementing Google OAuth 2.0 Sign-In and session management using JSON Web Tokens (JWT).

Changes Included

• Frontend: Added the Google Identity Services snippet and an official Google Sign-In button inside the existing auth-modal on index.html. It intercepts the successful login and forwards the token to the backend.
• Backend Verification: Implemented the /api/auth/google endpoint utilizing google-auth-library to securely verify the incoming token using Google's public keys.
• Session Management (JWT): Replaced the basic local login system with JWT-based session management, issuing 7-day tokens upon both Google and local logins.
• SQLite Database Support: Rather than introducing an entirely new MongoDB dependency just for users as suggested in the issue, a native users table was added inside the existing studyplan.db using SQLite to seamlessly store the Google profile data (email, name, picture, auth_provider) alongside the existing tasks and subjects.

How to Test

1. Set the GOOGLE_CLIENT_ID and JWT_SECRET in your .env file.
2. Run npm install to grab the newly added jsonwebtoken and google-auth-library dependencies.
3. Start the server via npm start.
4. Open the site, hit Sign In, and utilize the Google login button. Upon a successful login, an account will be created under the users table in SQLite and the session token will be saved to your local storage.