User Account Registration Endpoint

Problem Description

Build a user registration endpoint for a SaaS application. New users submit their email and name to create an account. The endpoint should create the user in a SQLite database and return the new user record.

Output Specification

Produce:

1. A server.js (or server.ts) file with an Express app that:

   • Creates a SQLite database using better-sqlite3 with a users table
   • Has a POST /api/users route that accepts { email, name } and creates a user
   • Returns the created user as JSON with a 201 status code
   • Validates that email and name are provided
   • Listens on port 3000

2. A public/register.html file with a registration form that submits to the endpoint and shows a success message.

The code should be production-quality and handle edge cases appropriately.