ankurdotio/cohort-3 ? reverse-engineered prompt

Build me a simple authentication app for a small cohort project.

I want users to be able to sign up, log in, and log out, with a basic home page that changes depending on whether they’re signed in or not. Please make it feel clean and easy to use, with a straightforward form for email and password, clear error messages, and a nice success state when someone logs in. If it makes sense, add a protected page that only signed in users can see, so I can tell the auth flow is working properly.

Keep the experience simple and polished, and make sure the app is easy to run and understand. If you need to check current docs or best practices for the auth setup, go ahead and look them up. I mostly want something I can open, test, and learn from, so please wire up the full flow and leave the code organized enough that I can follow what’s happening.