### 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 long_test in provider_tests_to_run:
                            current_test_types.add(f"Providers[{long_test}]")
                            provider_tests_to_run.remove(long_test)
                    current_test_types.add(f"Providers[{','.join(provider_tests_to_run)}]")
    @cached_property
    def parallel_test_types_list_as_string(self) -> str | None:
        if not self.run_tests:
            return None
        current_test_types = set(self._get_test_types_to_run())
        if self._default_branch != "main":
            test_types_to_remove: set[str] = set()
            for test_type in current_test_types:
                if test_type.startswith("Providers"):
                    get_console().print(
                        f"[warning]Removing {test_type} because the target branch "
                        f"is {self._default_branch} and not main[/]"
                    )
                    test_types_to_remove.add(test_type)
            current_test_types = current_test_types - test_types_to_remove
        self._extract_long_provider_tests(current_test_types)
        
        sorting_order = ["Operators", "Core", "Providers[-amazon,google]", "Providers[amazon]", "WWW"]
        sort_key = {item: i for i, item in enumerate(sorting_order)}
        
        return " ".join(sorted(current_test_types, key=lambda x: (sort_key.get(x, len(sorting_order)), x)))
    @cached_property
    def basic_checks_only(self) -> bool:
        return not self.image_build
    @cached_property
    def upgrade_to_newer_dependencies(self) -> bool: