### 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.
stderr = SelectiveChecks(
        files=(),
        commit_ref="",
        github_event=github_event,
        pr_labels=(),
        default_branch="main",
    )
    assert_outputs_are_printed(
        {
            "all-python-versions": "['3.8', '3.9', '3.10', '3.11']",
            "all-python-versions-list-as-string": "3.8 3.9 3.10 3.11",
            "image-build": "true",
            "needs-helm-tests": "true",
            "run-tests": "true",
            "docs-build": "true",
            "upgrade-to-newer-dependencies": "true"
            if github_event in [GithubEvents.PUSH, GithubEvents.SCHEDULE]
            else "false",
            "parallel-test-types-list-as-string": "Operators Core Providers[-amazon,google] "
            "Providers[amazon] WWW "
            "API Always CLI Other Providers[google]",
        },
        str(stderr),
    )
@pytest.mark.parametrize(
    "files, expected_outputs, pr_labels",
    [
        pytest.param(