Prepending `None` to sys.path breaks `importlib.metadata.version`

Bug report

Bug description:

import sys
sys.path.insert(0, None)
from importlib.metadata import version
print(version("requests"))

Results in

Traceback (most recent call last):
  File "<string>", line 1, in <module>
  File "/usr/lib/python3.12/importlib/metadata/__init__.py", line 889, in version
    return distribution(distribution_name).version
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/usr/lib/python3.12/importlib/metadata/__init__.py", line 862, in distribution
    return Distribution.from_name(distribution_name)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/usr/lib/python3.12/importlib/metadata/__init__.py", line 397, in from_name
    return next(cls.discover(name=name))
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/usr/lib/python3.12/importlib/metadata/__init__.py", line 795, in <genexpr>
    path.search(prepared) for path in map(FastPath, paths)
    ^^^^^^^^^^^^^^^^^^^^^
  File "/usr/lib/python3.12/importlib/metadata/__init__.py", line 693, in search
    return self.lookup(self.mtime).search(name)
                       ^^^^^^^^^^
  File "/usr/lib/python3.12/importlib/metadata/__init__.py", line 698, in mtime
    return os.stat(self.root).st_mtime
           ^^^^^^^^^^^^^^^^^^
TypeError: stat: path should be string, bytes, os.PathLike or integer, not NoneType

The documentation for sys.path is not clear on what should happen with non-strings in the list.

CPython versions tested on:

3.12

Operating systems tested on:

Linux

Start by reproducing the example, then read importlib.metadata around Distribution.from_name, FastPath.search, and FastPath.mtime as identified in the traceback. Check the sys.path documentation and related tests to determine the intended handling of non-string entries; done means the behavior is explicitly defined and covered by a regression test.