BUG: .str.len() does not work if the dtype is a pyarrow-backed list

[ddutt]

Pandas version checks

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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
import pyarrow as pa

df = pd.DataFrame({'a': pd.Series([[1, 2, 3], [4, 5, 6]],  dtype=pd.ArrowDtype(pa.list_(pa.int16())))})

df.a.str.len()

Issue Description

The above code aborts with the error: AttributeError: Can only use .str accessor with string values!

Expected Behavior

As per the description of str.len(), it should accept list-like dtypes to compute the length of each cell. If I use non-pyarrow backed lists, it works fine.

Installed Versions

In [7]: pd.show_versions() /work/.venv/lib/python3.11/site-packages/_distutils_hack/__init__.py:33: UserWarning: Setuptools is replacing distutils. warnings.warn("Setuptools is replacing distutils.")

INSTALLED VERSIONS

commit : e86ed37
python : 3.11.3.final.0
python-bits : 64
OS : Linux
OS-release : 6.2.0-33-generic
Version : #33~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Thu Sep 7 10:33:52 UTC 2
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.1.1
numpy : 1.26.0
pytz : 2023.3.post1
dateutil : 2.8.2
setuptools : 68.2.2
pip : 23.0
Cython : None
pytest : 7.4.2
hypothesis : 6.87.0
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.15.0
pandas_datareader : None
bs4 : None
bottleneck : None
dataframe-api-compat: None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 13.0.0
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : 2.0.21
tables : None
tabulate : 0.8.10
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None

[ddutt]

Duplicate of #55323