### 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.
if not self.full_tests_needed:
            
            return []
        return [
            
            {"python-version": python_version, "mssql-version": mssql_version}
            for python_version, mssql_version in excluded_combos(
                CURRENT_PYTHON_MAJOR_MINOR_VERSIONS, CURRENT_MSSQL_VERSIONS
            )
        ]
    @cached_property
    def mysql_exclude(self) -> list[dict[str, str]]:
        if not self.full_tests_needed:
            
            return []
        return [
            
            {"python-version": python_version, "mysql-version": mysql_version}
            for python_version, mysql_version in excluded_combos(
                CURRENT_PYTHON_MAJOR_MINOR_VERSIONS, CURRENT_MYSQL_VERSIONS
            )
        ]
    @cached_property
    def sqlite_exclude(self) -> list[dict[str, str]]: