Implement global authentication and local data sync

[MoonTree26]

Closes #281

Summary:

• Implemented email/password signup and login with hashed passwords and JWT responses.
• Added authenticated localStorage sync endpoints for pushing and reading user-local data on demand.
• Updated the auth page to store the authenticated user/token, auto-sync after login/signup, and expose a manual Sync Local Data button.
• Documented the API base URL and sync behavior in the README.

Validation:

• node --check backend/Controllers/auth/user_auth.js
• node --check backend/Middleware/auth.js
• node --check backend/Models/userModel.js
• node --check backend/Routers/router_auth.js
• git diff --check

Bounty claim:
This PR resolves the $10 bounty in #281.