### 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.
get_console().print("[yellow]You are modifying suspended providers.\n")
        get_console().print(
            "[info]Some providers modified by this change have been suspended, "
            "and before attempting such changes you should fix the reason for suspension."
        )
        get_console().print(
            "[info]When fixing it, you should set suspended = false in provider.yaml "
            "to make changes to the provider."
        )
        get_console().print(f"Suspended providers: {suspended_providers}")
        if fail_if_suspended_providers_affected:
            get_console().print(
                "[error]This PR did not have `allow suspended provider changes` label set so it will fail."
            )
            sys.exit(1)
        else:
            get_console().print(
                "[info]This PR had `allow suspended provider changes` label set so it will continue"
            )
    if not all_providers:
        return None
    for provider in list(all_providers):
        all_providers.update(
            get_related_providers(provider, upstream_dependencies=True, downstream_dependencies=True)
        )
    return sorted(all_providers)
class SelectiveChecks:
    __HASHABLE_FIELDS = {"_files", "_default_branch", "_commit_ref", "_pr_labels", "_github_event"}
    def __init__(