### 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.
"ubuntu-22.04",
            id="Push event for private repo",
        ),
        pytest.param(
            GithubEvents.PULL_REQUEST, "user", "apache/airflow", [], dict(), "ubuntu-22.04", id="Pull request"
        ),
        pytest.param(
            GithubEvents.PULL_REQUEST,
            "user",
            "private/airflow",
            [],
            dict(),
            "ubuntu-22.04",
            id="Pull request private repo",
        ),
        pytest.param(
            GithubEvents.PULL_REQUEST,
            COMMITTERS[0],
            "apache/airflow",
            [],
            dict(),
            "self-hosted",
            id="Pull request committer",
        ),
        pytest.param(
            GithubEvents.PULL_REQUEST,
            COMMITTERS[0],
            "apache/airflow",
            [],
            dict(event=dict(pull_request=dict(user=dict(login="user")))),