GH-104947: Make pathlib.PureWindowsPath comparisons consistent across platforms (GH-104948)

Use `str.lower()` rather than `ntpath.normcase()` to normalize case of
Windows paths. This restores behaviour from Python 3.11.

Co-authored-by: Gregory P. Smith <greg@krypto.org>

Lib/pathlib.py

diff --git a/Lib/pathlib.py b/Lib/pathlib.py
index fb78939..c893168 100644
--- a/Lib/pathlib.py
+++ b/Lib/pathlib.py
@@ -421,7 +421,10 @@ def _str_normcase(self):
         try:
             return self._str_normcase_cached
         except AttributeError:
-            self._str_normcase_cached = self._flavour.normcase(str(self))
+            if _is_case_sensitive(self._flavour):
+                self._str_normcase_cached = str(self)
+            else:
+                self._str_normcase_cached = str(self).lower()
             return self._str_normcase_cached
 
     @property

Lib/test/test_pathlib.py

diff --git a/Lib/test/test_pathlib.py b/Lib/test/test_pathlib.py
index 8b68cdc..ef202b7 100644
--- a/Lib/test/test_pathlib.py
+++ b/Lib/test/test_pathlib.py
@@ -904,6 +904,7 @@ def test_eq(self):
         self.assertEqual(P('a/B'), P('A/b'))
         self.assertEqual(P('C:a/B'), P('c:A/b'))
         self.assertEqual(P('//Some/SHARE/a/B'), P('//somE/share/A/b'))
+        self.assertEqual(P('\u0130'), P('i\u0307'))
 
     def test_as_uri(self):
         P = self.cls

Misc/NEWS.d/next/Library/2023-05-25-22-54-20.gh-issue-104947.hi6TUr.rst

diff --git a/Misc/NEWS.d/next/Library/2023-05-25-22-54-20.gh-issue-104947.hi6TUr.rst b/Misc/NEWS.d/next/Library/2023-05-25-22-54-20.gh-issue-104947.hi6TUr.rst
new file mode 100644
index 0000000..4af73d7
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2023-05-25-22-54-20.gh-issue-104947.hi6TUr.rst
@@ -0,0 +1,2 @@
+Make comparisons between :class:`pathlib.PureWindowsPath` objects consistent
+across Windows and Posix to match 3.11 behavior.