### Body

Same as https://github.com/apache/airflow/issues/33876 but for `publish-docs` command.

### Committer

- [X] I acknowledge that I am a maintainer/committer of the Apache Airflow project.
get_console().print("[info]Skipping latest image tagging as user requested it.[/]")
        else:
            get_console().print(
                "[info]Also tagging the images with latest tags as this is release version.[/]"
            )
    result_docker_buildx = run_command(
        ["docker", "buildx", "version"],
        check=False,
    )
    if result_docker_buildx.returncode != 0:
        get_console().print("[error]Docker buildx plugin must be installed to release the images[/]")
        get_console().print()
        get_console().print("See https://docs.docker.com/buildx/working-with-buildx/ for installation info.")
        sys.exit(1)
    result_inspect_builder = run_command(["docker", "buildx", "inspect", "airflow_cache"], check=False)
    if result_inspect_builder.returncode != 0:
        get_console().print("[error]Airflow Cache builder must be configured to release the images[/]")
        get_console().print()
        get_console().print(
            "See https://github.com/apache/airflow/blob/main/dev/MANUALLY_BUILDING_IMAGES.md"
            " for instructions on setting it up."
        )
        sys.exit(1)
    result_regctl = run_command(["regctl", "version"], check=False)
    if result_regctl.returncode != 0:
        get_console().print("[error]Regctl must be installed and on PATH to release the images[/]")
        get_console().print()
        get_console().print(
            "See https://github.com/regclient/regclient/blob/main/docs/regctl.md for installation info."
        )