Flutter Firebase Real-Time Chat

I need a clean, modern Flutter app that lets users exchange text messages in real time. Every user who signs up should instantly appear in a single public chat—no contact selection or private rooms. Core requirements are straightforward:

• Firebase Authentication handles sign-up and login.
• Messages live in Cloud Firestore and update instantly across devices.
• Each user can edit or delete only their own messages.
• UI stays simple, responsive, and visually consistent with current Flutter Material 3 guidelines.

Deliverables
• Complete, well-structured Flutter source code (Dart).
• Firebase project configuration for Auth and Firestore.
• A concise setup guide so I can run the project locally and deploy it to both Android and iOS.

Keep the code clean, comment where it matters, and avoid unnecessary packages; Firebase core, auth, and cloud_firestore should cover it. If anything in the brief seems unclear, let me know early so we can keep the build cycle tight and efficient.