String dtype: fix alignment sorting in case of python storage

Author: jorisvandenbossche

Diff for: pandas/core/indexes/base.py

@@ -4884,7 +4884,10 @@ def _can_use_libjoin(self) -> bool:
             return (
                 isinstance(self.dtype, np.dtype)
                 or isinstance(self._values, (ArrowExtensionArray, BaseMaskedArray))
-                or self.dtype == "string[python]"
+                or (
+                    isinstance(self.dtype, StringDtype)
+                    and self.dtype.storage == "python"
+                )
             )
         # Exclude index types where the conversion to numpy converts to object dtype,
         #  which negates the performance benefit of libjoin