String dtype: fix alignment sorting in case of python storage (#59448)

* String dtype: fix alignment sorting in case of python storage

* add test

Author: jorisvandenbossche

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

pandas/tests/series/methods/test_align.py

@@ -148,6 +148,19 @@ def test_align_periodindex(join_type):
     ts.align(ts[::2], join=join_type)
 
 
+def test_align_stringindex(any_string_dtype):
+    left = Series(range(3), index=pd.Index(["a", "b", "d"], dtype=any_string_dtype))
+    right = Series(range(3), index=pd.Index(["a", "b", "c"], dtype=any_string_dtype))
+    result_left, result_right = left.align(right)
+
+    expected_idx = pd.Index(["a", "b", "c", "d"], dtype=any_string_dtype)
+    expected_left = Series([0, 1, np.nan, 2], index=expected_idx)
+    expected_right = Series([0, 1, 2, np.nan], index=expected_idx)
+
+    tm.assert_series_equal(result_left, expected_left)
+    tm.assert_series_equal(result_right, expected_right)
+
+
 def test_align_left_fewer_levels():
     # GH#45224
     left = Series([2], index=pd.MultiIndex.from_tuples([(1, 3)], names=["a", "c"]))