Python 3.11 -P option changes one aspect of nspkg.pth namespace packages

Bug report

When trying to add the -P flag to Python shebangs in Fedora package, @befeleme discovered that our sphinxcontrib-programoutput fails to build documentation when /usr/bin/sphinx-build has -P in the shebang. After a lot of debugging, I've discovered that -P somewhat breaks the behavior wrt old-school namespace packages with nspkg.pth files.

To reproduce, I needed to install a sphinxcontrib-namespaced package globally to site-packages. Then, importing another sphinxcontrib-namespaced package without nspkg.pth from a manually specified $PYTHONPATH location fails with -P.

$ podman run --rm -ti python:3.11.0b3 /bin/bash
...
root@b881d08fc5f2:/# pip install 'sphinxcontrib-htmlhelp==2.0.0'
...
root@b881d08fc5f2:/# ls -1 /usr/local/lib/python3.11/site-packages
...
sphinxcontrib_htmlhelp-2.0.0-py3.9-nspkg.pth
sphinxcontrib_htmlhelp-2.0.0.dist-info
...
root@b881d08fc5f2:/# cd /tmp

root@b881d08fc5f2:/tmp# mkdir -p build/lib/sphinxcontrib/programoutput/
root@b881d08fc5f2:/tmp# touch build/lib/sphinxcontrib/programoutput/__init__.py

root@b881d08fc5f2:/tmp# PYTHONPATH=build/lib python3.11 -c 'import sphinxcontrib.programoutput'
(success)

root@b881d08fc5f2:/tmp# PYTHONPATH=build/lib python3.11 -P -c 'import sphinxcontrib.programoutput'
Traceback (most recent call last):
  File "<string>", line 1, in <module>
ModuleNotFoundError: No module named 'sphinxcontrib.programoutput'

When the import is in a script, it behaves the same:

root@b881d08fc5f2:/tmp# cat > script.py
import sphinxcontrib.programoutput

root@b881d08fc5f2:/tmp# PYTHONPATH=build/lib python3.11 script.py
(success)

root@b881d08fc5f2:/tmp# PYTHONPATH=build/lib python3.11 -P script.py 
Traceback (most recent call last):
  File "/tmp/script.py", line 1, in <module>
    import sphinxcontrib.programoutput
    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
ModuleNotFoundError: No module named 'sphinxcontrib.programoutput'

Your environment

I wasn't able to reproduce this in venv, only when installing the namespace packages globally to system-wide site-packages. I've reproduced on Fedora as well as in the official python:3.11.0b3 Docker image.

• CPython versions tested on: 3.11.0b3
• Operating system and architecture: Fedora Linux, Debian, x86_64

Start by reproducing the reported import failure with Python 3.11, -P, PYTHONPATH, and a globally installed nspkg.pth namespace package as shown. Trace how -P and site-packages path initialization interact, then verify that importing the manually supplied sphinxcontrib package succeeds without regressing the documented -P behavior.