Add an option to mount `airflow-site/sphinx_airflow_theme` when running CI locally

### Description

As of today, making changes in Airflow's site theme requires a lot of effort, as `sphinx_airflow_theme` is installed from PyPi: https://github.com/apache/airflow/blob/14f6622827c216a1091b24778e868598422ad9f1/hatch_build.py#L158

It doesn't happen often, but when we need to modify it for any reason (for example, as part of upgrading Sphinx version and related components - see this [PR](https://github.com/apache/airflow-site/pull/1103/files)), we need to make a lot of workarounds to make it work.
Having the option to mount local `airflow-site` directory will make it way easier to test.

### Use case/motivation

_No response_

### Related issues

_No response_

### Are you willing to submit a PR?

- [ ] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

Start with hatch_build.py at the linked dependency setup and trace the local CI path that uses sphinx_airflow_theme. Check the airflow-site repository and related PR for the expected mount behavior. Done means local CI has an option to mount airflow-site so theme changes can be tested without using the published package.

Written by the indexing model from the issue text.