Fix StringArray.astype for category dtype

pandas/core/arrays/string_.py

@@ -307,7 +307,6 @@ def __setitem__(self, key, value):
 
     def astype(self, dtype, copy=True):
         dtype = pandas_dtype(dtype)
-
         if is_dtype_equal(dtype, self.dtype):
             if copy:
                 return self.copy()
@@ -327,6 +326,9 @@ def astype(self, dtype, copy=True):
             arr[mask] = "0"
             values = arr.astype(dtype.numpy_dtype)
             return FloatingArray(values, mask, copy=False)
+        elif isinstance(dtype, ExtensionDtype):
+            cls = dtype.construct_array_type()
+            return cls._from_sequence(self, dtype=dtype, copy=copy)
         elif np.issubdtype(dtype, np.floating):
             arr = self._ndarray.copy()
             mask = self.isna()

pandas/tests/series/methods/test_astype.py

@@ -470,6 +470,18 @@ def test_astype_categories_raises(self):
         with pytest.raises(TypeError, match="got an unexpected"):
             s.astype("category", categories=["a", "b"], ordered=True)
 
+    def test_astype_str_to_extension_dtype(self):
+        # GH-40351
+        s = Series(["A", np.NaN], dtype="string")
+        result = s.astype("category")
+        expected = Series(["A", np.NaN], dtype="category")
+        tm.assert_series_equal(result, expected)
+
+        s = Series(["1/1/2021", "2/1/2021"], dtype="string")
+        result = s.astype("period[M]")
+        expected = Series(["1/1/2021", "2/1/2021"], dtype="period[M]")
+        tm.assert_series_equal(result, expected)
+
     @pytest.mark.parametrize("items", [["a", "b", "c", "a"], [1, 2, 3, 1]])
     def test_astype_from_categorical(self, items):
         ser = Series(items)