### 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.
cmd_to_run = ["/opt/airflow/scripts/in_container/run_prepare_provider_packages.sh", *packages_list]
    result_command = run_docker_command_with_debug(
        params=shell_params,
        command=cmd_to_run,
        debug=debug,
    )
    sys.exit(result_command.returncode)
def run_generate_constraints(
    shell_params: ShellParams,
    debug: bool,
    output: Output | None,
) -> tuple[int, str]:
    cmd_to_run = [
        "/opt/airflow/scripts/in_container/run_generate_constraints.sh",
    ]
    generate_constraints_result = run_docker_command_with_debug(
        params=shell_params,
        command=cmd_to_run,
        debug=debug,
        output=output,
        output_outside_the_group=True,
    )
    return (
        generate_constraints_result.returncode,
        f"Constraints {shell_params.airflow_constraints_mode}:{shell_params.python}",
    )
CONSTRAINT_PROGRESS_MATCHER = (
    r"Found|Uninstalling|uninstalled|Collecting|Downloading|eta|Running|Installing|built|Attempting"
)
def run_generate_constraints_in_parallel(