Bring back the PR Refactor doctests + add CI to main (#23271)

* Revert "Revert "[Doctests] Refactor doctests + add CI" (#23245)"

This reverts commit 69ee46243c.

* try not expose HfDocTestParser

* move into testing_utils.py

* remove pytest install

---------

Co-authored-by: ydshieh <ydshieh@users.noreply.github.com>

docs/source/en/testing.mdx

@@ -212,20 +212,12 @@ Example:
     ```"""
 
 ```
-3 steps are required to debug the docstring examples: 
-1. In order to properly run the test, **an extra line has to be added** at the end of the docstring. This can be automatically done on any file using: 
-```bash 
-python utils/prepare_for_doc_test.py <path_to_file_or_dir>
-```
 
-2. Then, you can use the following line to automatically test every docstring example in the desired file: 
+Just run the following line to automatically test every docstring example in the desired file: 
 ```bash 
 pytest --doctest-modules <path_to_file_or_dir>
 ```
-3. Once you are done debugging, you need to remove the extra line added in step **1.** by running the following: 
-```bash 
-python utils/prepare_for_doc_test.py <path_to_file_or_dir> --remove_new_line
-```
+If the file has a markdown extention, you should add the `--doctest-glob="*.mdx"` argument.
 
 ### Run only modified tests