### 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.
run_command(["git", "fetch", remote_name], cwd=constraints_repo)
def checkout_constraint_tag_and_reset_branch(constraints_repo: Path, airflow_version: str) -> None:
    run_command(
        ["git", "reset", "--hard"],
        cwd=constraints_repo,
    )
    
    run_command(
        ["git", "checkout", f"constraints-{airflow_version}"],
        cwd=constraints_repo,
    )
    
    run_command(
        ["git", "checkout", "-B", f"constraints-{airflow_version}-fix"],
        cwd=constraints_repo,
    )
    get_console().print(
        f"[info]Checked out constraints tag: constraints-{airflow_version} and "
        f"reset branch constraints-{airflow_version}-fix to it.[/]"
    )
    result = run_command(
        ["git", "show", "-s", "--format=%H"],
        cwd=constraints_repo,
        text=True,
        capture_output=True,
    )
    get_console().print(f"[info]The hash commit of the tag:[/] {result.stdout}")
def update_comment(content: str, comment_file: Path) -> str: