BUG: .dtypes are not copied on df.copy(deep=True)

[dchigarev]

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Reproducible Example

import modin.pandas as pd

df = pd.DataFrame({"a": [1, 2]})
df_renamed = df.rename(columns={"a": "new_a"}, copy=True, inplace=False)

# both `.dtypes` has changed
print(df_renamed.dtypes) # new_a: int64
print(df.dtypes) # new_a: int64

Issue Description

The PandasDataframe logic doesn't copy .dtypes as it should:

modin/modin/core/dataframe/pandas/dataframe/dataframe.py

Lines 1167 to 1174 in 91d6825

	return self.__constructor__(
	self._partitions,
	self._index_cache.copy() if self._index_cache is not None else None,
	self._columns_cache.copy() if self._columns_cache is not None else None,
	self._row_lengths_cache,
	self._column_widths_cache,
	self._dtypes,
	)

Expected Behavior

df.dtypes is df.copy().dtypes == False

Error Logs

Replace this line with the error backtrace (if applicable).

Installed Versions

Replace this line with the output of pd.show_versions()