Kalvabhavik/sbchat ? reverse-engineered prompt

Build me a Flutter chat app called Neon City Chat that feels fast, modern, and a little futuristic. I want users to be able to sign up, log in, and send messages in real time through Firebase, with chats updating instantly. Keep the interface clean and polished, with smooth animations, stylish typography, and a glassy neon inspired look that works well on both Android and iPhone.

Please make the app feel like a real finished product, with a simple flow from authentication into the main chat experience, and a responsive layout that still looks good on different screen sizes. If you need to check anything current about Flutter or Firebase setup, look up the latest docs online.