Fix GH-29442 DataFrame.groupby doesn't preserve _metadata

This bug is a regression in v1.1.0 and was introduced by the fix for GH-34214 in commit [6f065b].

Underlying cause is that the `*Splitter` classes do not use the `._constructor` property and do not call `__finalize__`.

Please note that the method name used for `__finalize__` calls was my best guess since documentation for the value has been hard to find.

[6f065b]: 6f065b6

pandas/core/groupby/ops.py

@@ -955,7 +955,8 @@ class SeriesSplitter(DataSplitter):
     def _chop(self, sdata: Series, slice_obj: slice) -> Series:
         # fastpath equivalent to `sdata.iloc[slice_obj]`
         mgr = sdata._mgr.get_slice(slice_obj)
-        return type(sdata)(mgr, name=sdata.name, fastpath=True)
+        return sdata._constructor(mgr, name=sdata.name, fastpath=True)\
+            .__finalize__(sdata, method='groupby')
 
 
 class FrameSplitter(DataSplitter):
@@ -971,7 +972,7 @@ def _chop(self, sdata: DataFrame, slice_obj: slice) -> DataFrame:
         # else:
         #     return sdata.iloc[:, slice_obj]
         mgr = sdata._mgr.get_slice(slice_obj, axis=1 - self.axis)
-        return type(sdata)(mgr)
+        return sdata._constructor(mgr).__finalize__(sdata, method='groupby')
 
 
 def get_splitter(

pandas/tests/groupby/test_custom_metadata.py

@@ -0,0 +1,83 @@
+"""
+Test metadata propagation in groupby
+
+The PandasTable class below is implemented according to the [guidelines], and as such would
+expect `__finalize__` to always be called so that the `_pandastable_metadata` is always populated. 
+
+[guidelines]: https://pandas.pydata.org/pandas-docs/stable/development/extending.html#override-constructor-properties
+"""
+
+import pytest
+import pandas as pd
+from warnings import warn
+from typing import List
+
+
+_TABLE_METADATA_FIELD_NAME = '_pandastable_metadata'
+
+
+def _combine_metadata(data: List[str]) -> str:
+    """
+    A mock implementation for testing
+    """
+    return '+'.join(data)
+
+
+class PandasTable(pd.DataFrame):
+    """
+    A pandas dataframe subclass with associated table metadata.
+    """
+
+    _metadata = [_TABLE_METADATA_FIELD_NAME]  # Register metadata fieldnames here
+
+    @property
+    def _constructor(self):
+        return PandasTable
+
+    def __finalize__(self, other, method=None, **kwargs):
+        """
+        This method is responsible for populating metadata when creating new Table-object.
+
+        The method argument is subject to change, and a robust handling of this is implemented
+        """
+        src = [other] #more logic here in actual implementation
+        metadata = _combine_metadata([d.get_metadata() for d in src if isinstance(d, PandasTable)])
+
+        if not metadata:
+            warn('__finalize__ unable to combine metadata for method "{method}", falling back to DataFrame')
+            return pd.DataFrame(self)
+        object.__setattr__(self, _TABLE_METADATA_FIELD_NAME, metadata)
+        return self
+
+    def get_metadata(self):
+        #return object.__getattribute__(self, _TABLE_METADATA_FIELD_NAME)
+        metadata = getattr(self, _TABLE_METADATA_FIELD_NAME, None)
+        if metadata is None:
+            warn('PandasTable object not correctly initialized: no metadata')
+        return metadata
+
+    @staticmethod
+    def from_table_data(df: pd.DataFrame, metadata) -> 'PandasTable':
+        df = PandasTable(df)
+        object.__setattr__(df, _TABLE_METADATA_FIELD_NAME, metadata)
+        return df
+
+
+@pytest.fixture
+def dft():
+    df = pd.DataFrame([[11, 12, 0], [21, 22, 0], [31, 32, 1]], columns={'a','b','g'})
+    return PandasTable.from_table_data(df, 'My metadata')    
+
+
+def test_initial_metadata(dft):
+    assert dft.get_metadata() == 'My metadata'
+
+
+def test_basic_propagation(dft):
+    gg = dft.loc[dft.g==0, :]
+    assert gg.get_metadata() == 'My metadata'
+
+
+def test_groupby(dft):
+    gg = [ab for g, ab in dft.groupby('g')]
+    assert gg[0].get_metadata() is not None