### Pandas version checks - [X] I have checked that this issue has not already been reported. - [X] I have confirmed this bug exists on the [latest version](https://pandas.pydata.org/docs/whatsnew/index.html) of pandas. - [X] I have confirmed this bug exists on the [main branch](https://pandas.pydata.org/docs/dev/getting_started/install.html#installing-the-development-version-of-pandas) of pandas. ### Reproducible Example ```python import numpy as np import pickle from pandas._libs.lib import ensure_string_array t = np.array([None, None, {'a': 1.235}]) tp = pickle.loads(pickle.dumps(t)) g = np.asarray(tp, dtype='object') assert g is not tp assert np.shares_memory(g, tp) print(tp) # Expected [None, None, {'a': 1.235}] print(ensure_string_array(tp)) # got [nan, nan, "{'a': 1.235}"] print(tp) # Expected [None, None, {'a': 1.235}], got [nan, nan, "{'a': 1.235}"] ``` ### Issue Description I've had an issue where `df.astype(str)` actually changed `df` in-place instead of only making a copy. I've looked into where the values mutate and I found out that it originates in the cython implementation of `ensure_string_array`. * the validation on result is only using `arr is not result` to determine whether to copy the data * while this condition may be false for `result = np.asarray(arr, dtype='object')` - it may still share memory verified with `np.shares_memory(arr, result)` * I suggest to add/alter the condition with `np.shares_memory`. I tried to make a code that replicates the issue with the `astype()` example, but I didn't manage to do it easily. I can also make a PR if the solution sounds good to you. BTW, I'm not sure why the pickle loads/dumps change the behaviour here, but the example doesn't work without it ### Expected Behavior `astype()` should return a copy, if not specified otherwise `ensure_string_array()` should return a copy, if not specified otherwise ### Installed Versions <details> INSTALLED VERSIONS ------------------ commit : 37ea63d540fd27274cad6585082c91b1283f963d python : 3.10.11.final.0 python-bits : 64 OS : Linux OS-release : 6.2.0-26-generic Version : #26~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Thu Jul 13 16:27:29 UTC 2 machine : x86_64 processor : x86_64 byteorder : little LC_ALL : None LANG : en_US.UTF-8 LOCALE : en_US.UTF-8 pandas : 2.0.1 numpy : 1.24.3 pytz : 2023.3 dateutil : 2.8.2 setuptools : 57.5.0 pip : 22.3.1 Cython : 0.29.36 pytest : 7.3.1 hypothesis : None sphinx : None blosc : None feather : None xlsxwriter : 3.1.2 lxml.etree : 4.9.3 html5lib : None pymysql : None psycopg2 : None jinja2 : 3.1.2 IPython : 8.13.2 pandas_datareader: None bs4 : 4.12.2 bottleneck : 1.3.7 brotli : fastparquet : None fsspec : 2023.6.0 gcsfs : 2023.6.0 matplotlib : 3.7.2 numba : 0.57.1 numexpr : 2.8.4 odfpy : None openpyxl : 3.1.2 pandas_gbq : 0.17.9 pyarrow : 9.0.0 pyreadstat : None pyxlsb : 1.0.10 s3fs : None scipy : 1.10.1 snappy : sqlalchemy : None tables : 3.8.0 tabulate : None xarray : 2023.6.0 xlrd : 2.0.1 zstandard : 0.21.0 tzdata : 2023.3 qtpy : None pyqt5 : None </details>