Implement Amplify Auth with Cognito and Amplify UI React

**Goal:**
Add user authentication to the front-end using AWS Amplify Auth integrated with Cognito and Amplify UI React components for a secure and seamless experience.

**Scope:**
- Integrate Amplify into the Next.js (or React) front-end.
- Set up Amplify Auth to connect to an Amazon Cognito User Pool.
- Use Amplify UI React components for sign-up, sign-in, and password recovery forms.
- Ensure support for email/password authentication (Google/Apple OAuth can be “future”).
- Ensure authentication gates/protected routes for app pages after successful login.
- Add basic form validation and clear error/success feedback.
- Document setup and configuration steps (Amplify CLI, env vars, Cognito configuration).