### 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.mark.parametrize(
    "files, expected_outputs,",
    [
        pytest.param(
            ("docs/apache-airflow-providers-google/docs.rst",),
            {
                "docs-filter-list-as-string": "--package-filter apache-airflow-providers-amazon "
                "--package-filter apache-airflow-providers-apache-beam "
                "--package-filter apache-airflow-providers-apache-cassandra "
                "--package-filter apache-airflow-providers-cncf-kubernetes "
                "--package-filter apache-airflow-providers-common-sql "
                "--package-filter apache-airflow-providers-facebook "
                "--package-filter apache-airflow-providers-google "
                "--package-filter apache-airflow-providers-hashicorp "
                "--package-filter apache-airflow-providers-microsoft-azure "
                "--package-filter apache-airflow-providers-microsoft-mssql "
                "--package-filter apache-airflow-providers-mysql "
                "--package-filter apache-airflow-providers-openlineage "
                "--package-filter apache-airflow-providers-oracle "
                "--package-filter apache-airflow-providers-postgres "
                "--package-filter apache-airflow-providers-presto "
                "--package-filter apache-airflow-providers-salesforce "
                "--package-filter apache-airflow-providers-samba "
                "--package-filter apache-airflow-providers-sftp "
                "--package-filter apache-airflow-providers-ssh "
                "--package-filter apache-airflow-providers-trino",
            },
            id="Google provider docs changed",
        ),
        pytest.param(