Create a Python command-line application in the `~/shell/docker-manager/` directory to manage Docker containers defined in subdirectories of `~/docker/`. Each subdirectory contains either a `docker-compose.yml` or `compose.yml` file. The application must:

- List the names of currently running containers defined in `~/docker/`.
- Provide commands to stop, update (pull latest images), and restart these containers.
- Be executable from any directory via the command line, without requiring navigation to the script's location.
- Output results and status messages to the console.
- Include setup instructions for installation and usage.

Provide complete Python code and a `README.md` with setup and usage instructions. Use only files within `~/shell/docker-manager/` to avoid cluttering other directories. Reference the [Docker Compose CLI documentation](https://docs.docker.com/compose/reference/) for command usage.