### 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.
shell_params: ShellParams,
    cmd_to_run: list[str],
    list_of_providers: list[str],
    output: Output | None,
) -> tuple[int, str]:
    shell_params.install_selected_providers = " ".join(list_of_providers)
    result_command = run_docker_command_with_debug(
        params=shell_params,
        command=cmd_to_run,
        debug=False,
        output=output,
    )
    return result_command.returncode, f"{list_of_providers}"
SDIST_INSTALL_PROGRESS_REGEXP = r"Processing .*|Requirement already satisfied:.*|  Created wheel.*"
@release_management.command(