### Body

The `--package-filter` while nice in theory to specify which packages to build, has quite bad UX (lots of repetitions when specifying multiple packages, long package names. We practically (except `--package-filter apache-airflow-providers-*` never use the functionality of the filter with glob patterns.

It's much more practical to use "short" package names ("apache.hdfs" rather that `--package-filter apache-airflow-providers-apache-hdfs` and we already use it in a few places in Breeze. 

We should likely replace all the places when we use `--package-filter` with those short names, add a special alias for `all-providers` and this should help our users who build documentation and release manager to do their work faster and nicer. 

This would also allow to remove the separate ./dev/provider_packages/publish_provider_documentation.sh  bash script that is aimed to do somethign similar in a "hacky way".

### Committer

- [X] I acknowledge that I am a maintainer/committer of the Apache Airflow project.
build_errors: dict[str, list[DocBuildError]],
    spelling_errors: dict[str, list[SpellingError]],
) -> None:
    """Prints build errors and exists."""
    if build_errors or spelling_errors:
        if build_errors:
            display_errors_summary(build_errors)
            console.print()
        if spelling_errors:
            display_spelling_error_summary(spelling_errors)
            console.print()
        console.print("The documentation has errors.")
        display_packages_summary(build_errors, spelling_errors)
        console.print()
        console.print(CHANNEL_INVITATION)
        sys.exit(1)
    else:
        console.print("[green]Documentation build is successful[/]")
def main():
    """Main code"""
    args = _get_parser().parse_args()
    available_packages = get_available_packages()
    docs_only = args.docs_only
    spellcheck_only = args.spellcheck_only
    disable_provider_checks = args.disable_provider_checks
    disable_checks = args.disable_checks
    package_filters = args.package_filter
    with with_group("Available packages"):
        for pkg in sorted(available_packages):
            console.print(f" - {pkg}")