String dtype: fix alignment sorting in case of python storage

Author: jorisvandenbossche

pandas/core/generic.py

@@ -9542,7 +9542,6 @@ def _align_series(
                 join_index, lidx, ridx = self.index.join(
                     other.index, how=join, level=level, return_indexers=True
                 )
-
             if is_series:
                 left = self._reindex_indexer(join_index, lidx)
             elif lidx is None or join_index is None:

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