Guide the user through containerizing and serving a simple website or documentation folder with Docker — inspects the project to detect what to serve (ready-to-serve static HTML, a buildable site that emits static output, or a raw markdown/docs folder that needs rendering), generates a Dockerfile, .dockerignore, docker-compose.yml, helper run/build commands, and a 'Running with Docker' README section, then offers to build and smoke-test the container and publish the image to Docker Hub or GHCR. Uses nginx:alpine for static content and a multi-stage build when the site must be generated. Only invoke when the user explicitly types /ai-assist-dockerize-website. Never auto-trigger from general conversation about Docker, containers, websites, or Dockerfiles.