Implement user authentication and registration

Allow users to create accounts with a unique username and secure password. Provide login and registration forms, validate user inputs, and store user credentials securely.

## Expectations

- Users can register with a unique username and a strong password.
- Users can log in with their registered credentials.
- Passwords are hashed and stored securely in the database.

The issue identifies registration and login forms plus secure credential storage as the entry points; first inspect the existing TypeScript/React front end and Rails/PostgreSQL backend to find where account flows belong. Done means unique usernames, validated strong passwords, working login, and securely hashed credentials stored in the database.

Written by the indexing model from the issue text.