### Body

We need a small improvement for our docs publishing process.

We currently have those two scripts:

* [x] docs/publish_docs.py https://github.com/apache/airflow/blob/main/docs/publish_docs.py in airflow repo
* [ ] post-docs/ in airflow-site https://github.com/apache/airflow-site/blob/main/post-docs/add-back-references.py

We have currently the steps that are describing how to publish the documentation in our release documentation:

* https://github.com/apache/airflow/blob/main/dev/README_RELEASE_AIRFLOW.md
* https://github.com/apache/airflow/blob/main/dev/README_RELEASE_PROVIDER_PACKAGES.md
* https://github.com/apache/airflow/blob/main/dev/README_RELEASE_HELM_CHART.md

This is the "Publish documentation"  chapter

They currently consists of few steps:

1) checking out the main in "airflow-sites"
2) setting the AIRFLOW_SITE_DIRECTORY env variable to the checked out repo
3) building docs (with `breeze build-docs`) 
4) Running publish_docs.py scripts in docs that copies the generated docs to "AIRFLOW_SITE_DIRECTORY" 
5) **I just added those** running post-docs post-processing for back references
6) Commiting the changes and pushing them to airflow-site

(there are few variants of those depends what docs you are building).

The problem with that is that it requires several venvs to setup independently (and they might sometimes miss stuff) and those commands are distributed across repositories. 


The goal of the change is to replace publish + post-docs with single, new breeze command - similarly as we have "build-docs" now.

I imagine this command should be similar to:

```
breeze publish-docs --airflow-site-directory DIRECTORY --package-filter .... and the rest of other arguments that publish_docs.py has 
```

This command should copy the files and run post-processing on back-references (depending which package documentation we publish).

Then the process of publish docs should like:

1) checking out the main in "airflow-sites"
2) setting the AIRFLOW_SITE_DIRECTORY env variable to the checked out repo
3) building docs (with `breeze build-docs`) 
4) publishing docs (with `breeze publish-docs`) 
5) Commiting the changes and pushing them to airflow-site

The benefits:

* no separate venvs to manage (all done in breeze's env) - automatically manged
* nicer integration in our dev/CI environment
* all code for publishing docs in one place - in breeze




### Committer

- [X] I acknowledge that I am a maintainer/committer of the Apache Airflow project.
package_format: str,
    version_suffix_for_pypi: str,
    debug: bool,
    github_repository: str,
):
    perform_environment_checks()
    cleanup_python_generated_files()
    assert_pre_commit_installed()
    run_compile_www_assets(dev=False, run_in_background=False)
    shell_params = ShellParams(
        github_repository=github_repository,
        python=DEFAULT_PYTHON_MAJOR_MINOR_VERSION,
        package_format=package_format,
        version_suffix_for_pypi=version_suffix_for_pypi,
        skip_environment_initialization=True,
        install_providers_from_sources=False,
        mount_sources=MOUNT_ALL,
    )
    rebuild_or_pull_ci_image_if_needed(command_params=shell_params)
    result_command = run_docker_command_with_debug(
        params=shell_params,
        command=["/opt/airflow/scripts/in_container/run_prepare_airflow_packages.sh"],
        debug=debug,
        output_outside_the_group=True,