### 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.
pytest.param(
            ("docs/apache-airflow-providers-airbyte/docs.rst",),
            {
                "docs-filter-list-as-string": "--package-filter apache-airflow-providers-airbyte "
                "--package-filter apache-airflow-providers-http",
            },
            id="Airbyte provider docs changed",
        ),
        pytest.param(
            ("docs/apache-airflow-providers-airbyte/docs.rst", "docs/apache-airflow/docs.rst"),
            {
                "docs-filter-list-as-string": "--package-filter apache-airflow "
                "--package-filter apache-airflow-providers-airbyte "
                "--package-filter apache-airflow-providers-http",
            },
            id="Airbyte provider and airflow core docs changed",
        ),
        pytest.param(
            (
                "docs/apache-airflow-providers-airbyte/docs.rst",
                "docs/apache-airflow/docs.rst",
                "docs/apache-airflow-providers/docs.rst",
            ),
            {
                "docs-filter-list-as-string": "--package-filter apache-airflow "
                "--package-filter apache-airflow-providers "
                "--package-filter apache-airflow-providers-airbyte "
                "--package-filter apache-airflow-providers-http",
            },
            id="Airbyte provider and airflow core and common provider docs changed",