BUG: regression when applying groupby aggregation on categorical columns

pandas/core/arrays/base.py

@@ -47,7 +47,7 @@ def try_cast_to_ea(cls_or_instance, obj, dtype=None):
     ExtensionArray or obj
     """
     try:
-        result = cls_or_instance._from_sequence(obj, dtype=dtype)
+        result = cls_or_instance._from_sequence(obj, dtype=dtype.name)
     except Exception:
         # We can't predict what downstream EA constructors may raise
         result = obj

pandas/core/groupby/groupby.py

@@ -807,7 +807,10 @@ def _try_cast(self, result, obj, numeric_only: bool = False):
             dtype = obj.dtype
 
         if not is_scalar(result):
-            if is_extension_array_dtype(dtype) and dtype.kind != "M":
+            if (
+                is_extension_array_dtype(dtype)
+                and dtype.kind != "M"
+            ):
                 # The function can return something of any type, so check
                 #  if the type is compatible with the calling EA.
                 # datetime64tz is handled correctly in agg_series,

pandas/tests/groupby/test_categorical.py

@@ -1342,3 +1342,24 @@ def test_series_groupby_categorical_aggregation_getitem():
     result = groups["foo"].agg("mean")
     expected = groups.agg("mean")["foo"]
     tm.assert_series_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    "func, expected_values",
+    [(pd.Series.nunique, [1, 1, 2]), (pd.Series.count, [1, 2, 2])],
+)
+def test_groupby_agg_categorical_columns(func, expected_values):
+    # 31256
+    df = pd.DataFrame(
+        {
+            "id": [0, 1, 2, 3, 4],
+            "groups": [0, 1, 1, 2, 2],
+            "value": pd.Categorical([0, 0, 0, 0, 1]),
+        }
+    ).set_index("id")
+    result = df.groupby("groups").agg(func)
+
+    expected = pd.DataFrame(
+        {"value": expected_values}, index=pd.Index([0, 1, 2], name="groups")
+    )
+    tm.assert_frame_equal(result, expected)