Setting private class module name ignores class attribute docstrings

[cimes-isi]

Describe the bug

Per [1], automodule with the members option will document members with __module__ set to the module's name. However, docstrings of private class attributes (where the class has __module__ set) are ignored, even though the class is correctly documented and the attribute name appears.

[1] https://www.sphinx-doc.org/en/master/usage/extensions/autodoc.html

How to Reproduce

$ git clone https://github.com/cimes-isi/sphinx-private-module-class-field-docstring.git
$ cd sphinx-private-module-class-field-docstring
$ pip install sphinx
$ cd docs
$ make html

Open docs/build/html/testmod.html and see that ClassPrivate.foo is missing its docstring.

Expected behavior

The class attributes' docstrings should appear in the generated documentation.

Your project

https://github.com/cimes-isi/sphinx-private-module-class-field-docstring

Screenshots

OS

MacOS Big Sur

Python version

3.8.2

Sphinx version

4.3.1

Sphinx extensions

sphinx.ext.autodoc

Extra tools

No response

Additional context

No response