Next.js Authentication Feature Build

My current Next.js code-base is running smoothly, but it still needs a full user-account flow. I want to add:

• Email-and-password sign-up and login, including secure password hashing and session handling (NextAuth, bcrypt, or a comparable library are fine—feel free to suggest the best fit).
• A protected profile page that pulls user data from our existing API layer and only renders for authenticated sessions.
• Basic account management (update password, update profile details) so users can handle their own information without touching the database directly.

I will supply a clean branch of the repo, existing UI components, and an API endpoint for user CRUD. Your task is to wire everything together, ensure pages are fully responsive, and document any new environment variables or routes you introduce.

Acceptance criteria
– New routes build and run with yarn dev without errors.
– Registration, login, logout, and profile update processes succeed end-to-end.
– Unauthenticated visitors are redirected to the login page.
– All new code is TypeScript-strict and passes eslint/prettier checks.
– A short README section explains setup, environment variables, and how to extend the auth flow later.

Once these are met and merged via pull request, the milestone is complete.