### Body

Our CI generates `--package-filter` list in selective checks in order to pass them to `build-docs` and `publish-docs` commands. However after implementing #33876 and #34085 we could switch both commands to use short package ids which we already have (almost - there should be a slight modification for `apache-airflow`, `apache-airflow-providers` and `helm-chart` most likely. This should also simplify some of the unit tests we have.



### Committer

- [X] I acknowledge that I am a maintainer/committer of the Apache Airflow project.
file_path = AIRFLOW_SOURCES_ROOT / changed_file
    
    for provider_root in (TESTS_PROVIDERS_ROOT, SYSTEM_TESTS_PROVIDERS_ROOT, AIRFLOW_PROVIDERS_ROOT):
        try:
            file_path.relative_to(provider_root)
            relative_base_path = provider_root
            break
        except ValueError:
            pass
    else:
        if include_docs:
            try:
                relative_path = file_path.relative_to(DOCS_DIR)
                if relative_path.parts[0].startswith("apache-airflow-providers-"):
                    return relative_path.parts[0].replace("apache-airflow-providers-", "").replace("-", ".")
            except ValueError:
                pass
        return None
    for parent_dir_path in file_path.parents:
        if parent_dir_path == relative_base_path:
            break
        relative_path = parent_dir_path.relative_to(relative_base_path)
        if (AIRFLOW_PROVIDERS_ROOT / relative_path / "provider.yaml").exists():
            return str(parent_dir_path.relative_to(relative_base_path)).replace(os.sep, ".")
    
    return "Providers"
def find_all_providers_affected(