BUG:Pandas: Custom Metadata in DataFrame Subclass Not Deep-Copied

[Qi-henry]

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• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd


class MyDataFrame(pd.DataFrame):
    _metadata = [
        'name',
        'extra_info',
    ]

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.name = None
        self.extra_info = {}

    @property
    def n_unique_wafer(self):
        if 'wafer' in self.columns:
            return len(self['wafer'].unique())
        else:
            return None

    @property
    def _constructor(self):

        return MyDataFrame


if __name__ == "__main__":
    data = {
        'A': [1, 2, 3, 1, 2],
        'B': ['A', 'B', 'A', 'C', 'B']
    }

    df = MyDataFrame(data)

    df.extra_info = {"source": "Lab Experiment"}

    # test copy()
    copied_df = df.copy()
    df.extra_info["source"] = 'a'

    print("Extra Info:", copied_df.extra_info)
    print("df Extra Info:", df.extra_info)  # extra_info in df is changed

Issue Description

When using a custom subclass of pandas.DataFrame with additional metadata attributes (e.g., extra_info declared in _metadata), calling df.copy() or df.copy(deep=True) does not deep-copy the custom metadata attributes. Instead, the metadata remains shallow-copied, causing unintended shared references between the original and copied DataFrames.

Expected Behavior

Expected:
copied_df.extra_info should retain the original value {"source": "Original Data"}.
df.extra_info modifications should not affect the copy.
Actual:
Both the original and copied DataFrame share the same metadata object.
df.copy(deep=True) does not deep-copy the _metadata attributes.

Installed Versions

INSTALLED VERSIONS

commit : c888af6
python : 3.9.13
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.19045
machine : AMD64
processor : Intel64 Family 6 Model 183 Stepping 1, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE :

pandas : 2.3.1
numpy : 1.26.4
pytz : 2024.2
dateutil : 2.9.0.post0
pip : 25.1.1
Cython : 3.0.12
sphinx : None
IPython : 8.18.1
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : None
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
html5lib : None
hypothesis : None
gcsfs : None
jinja2 : 3.1.4
lxml.etree : 5.3.0
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 20.0.0
pyreadstat : None
pytest : 8.3.4
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.13.1
sqlalchemy : None
tables : None
tabulate : 0.9.0
xarray : None
xlrd : None
xlsxwriter : 3.2.0
zstandard : None
tzdata : 2025.2
qtpy : 2.4.2
pyqt5 : None