Add test for GH-37343

See https://pandas.pydata.org/pandas-docs/stable/development/extending.html#override-constructor-properties

Author: Japanuspus

pandas/tests/groupby/test_grouping.py

@@ -963,3 +963,18 @@ def test_grouping_string_repr(self):
         result = gr.grouper.groupings[0].__repr__()
         expected = "Grouping(('A', 'a'))"
         assert result == expected
+
+
+def test_groupby_iter_metadata():
+    # GH-37343
+    class SubclassedDataFrame2(DataFrame):
+        _metadata = ["_added_property"]
+
+        @property
+        def _constructor(self):
+            return SubclassedDataFrame2
+
+    custom_df = SubclassedDataFrame2({"a": [1, 2, 3], "b": [1, 1, 2], "c": [7, 8, 9]})
+    custom_df._added_property = "hello"
+    for _, group_df in custom_df.groupby("c"):
+        assert group_df._added_property == "hello"