[BUG]: pip uninstall pybind11[global] does not cleanly remove all pybind files

Required prerequisites

• Make sure you've read the documentation. Your issue may be addressed there.
• Search the issue tracker and Discussions to verify that this hasn't already been reported. +1 or comment there if it has.
• Consider asking first in the Gitter chat room or in a Discussion.

What version (or hash if on master) of pybind11 are you using?

2.11.1

Problem description

If we pip install pybind11[global], then pip uninstall pybind11[global] does not remove all pybind files.

Reproducible example code

$ python3.11 -m venv .
$ source bin/activate
$ pip install pybind11[global]
$ pip uninstall -y pybind11[global]
$ ls $VIRTUAL_ENV/include/pybind11/
attr.h                      detail/                     gil.h                       pytypes.h
buffer_info.h               eigen/                      iostream.h                  stl/
cast.h                      eigen.h                     numpy.h                     stl.h
chrono.h                    embed.h                     operators.h                 stl_bind.h
common.h                    eval.h                      options.h                   type_caster_pyobject_ptr.h
complex.h                   functional.h                pybind11.h

Is this a regression? Put the last known working version here if it is.

Not a regression

Start by reproducing the documented Python 3.11 virtual-environment commands with pybind11[global], then inspect which installed files remain after uninstall. Trace the package-installation metadata responsible for the global headers. Done means uninstalling pybind11[global] removes the pybind11 files from the virtual environment; the issue names no source files or tests.