BUG: arrow StructArray-backed object cannot be displayed

[a-reich]

Pandas version checks

• I have checked that this issue has not already been reported.

• 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, pyarrow as pa
struct = pa.StructArray.from_arrays(([1,2],['x','y']),names='ab')
pd.Series(struct, dtype=pd.ArrowDtype(struct.type)) # doesn't show anything on REPL, or
print(pd.Series(struct, dtype=pd.ArrowDtype(struct.type)))
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
<ipython-input-24-28e3429359af> in <module>
----> 1 print(pd.Series(struct, dtype=pd.ArrowDtype(struct.type)))

~\Miniconda3\envs\test\lib\site-packages\pandas\core\series.py in __repr__(self)
   1630         # pylint: disable=invalid-repr-returned
   1631         repr_params = fmt.get_series_repr_params()
-> 1632         return self.to_string(**repr_params)
   1633
   1634     @overload

~\Miniconda3\envs\test\lib\site-packages\pandas\core\series.py in to_string(self, buf, na_rep, float_format, header, index, length, dtype, name, max_rows, min_rows)
   1723             max_rows=max_rows,
   1724         )
-> 1725         result = formatter.to_string()
   1726
   1727         # catch contract violations

~\Miniconda3\envs\test\lib\site-packages\pandas\io\formats\format.py in to_string(self)
    391
    392         fmt_index, have_header = self._get_formatted_index()
--> 393         fmt_values = self._get_formatted_values()
    394
    395         if self.is_truncated_vertically:

~\Miniconda3\envs\test\lib\site-packages\pandas\io\formats\format.py in _get_formatted_values(self)
    375
    376     def _get_formatted_values(self) -> list[str]:
--> 377         return format_array(
    378             self.tr_series._values,
    379             None,

~\Miniconda3\envs\test\lib\site-packages\pandas\io\formats\format.py in format_array(values, formatter, float_format, na_rep, digits, space, justify, decimal, leading_space, quoting, fallback_formatter)
   1290     """
   1291     fmt_klass: type[GenericArrayFormatter]
-> 1292     if is_datetime64_dtype(values.dtype):
   1293         fmt_klass = Datetime64Formatter
   1294     elif isinstance(values.dtype, DatetimeTZDtype):

~\Miniconda3\envs\test\lib\site-packages\pandas\core\dtypes\common.py in is_datetime64_dtype(arr_or_dtype)
    304         # GH#33400 fastpath for dtype object
    305         return arr_or_dtype.kind == "M"
--> 306     return _is_dtype_type(arr_or_dtype, classes(np.datetime64))
    307
    308

~\Miniconda3\envs\test\lib\site-packages\pandas\core\dtypes\common.py in _is_dtype_type(arr_or_dtype, condition)
   1526
   1527     try:
-> 1528         tipo = pandas_dtype(arr_or_dtype).type
   1529     except (TypeError, ValueError):
   1530         if is_scalar(arr_or_dtype):

~\Miniconda3\envs\test\lib\site-packages\pandas\core\arrays\arrow\dtype.py in type(self)
    146             return type(pa_type)
    147         else:
--> 148             raise NotImplementedError(pa_type)
    149
    150     @property

NotImplementedError: struct<a: int64, b: string>

Issue Description

If one creates a pandas object with a dtype corresponding to a pyarrow struct type, it can be created and e.g. its .values can be accessed as a ArrowExtensionArray which displays, but it cannot be displayed with either __repr__ which shows None, or print() which raises.
This is quite similar to #48238, but I opened a new issue since that's closed already.

I also understand if the response is "we don't support arrow StructType yet" :-)
Thanks!

Expected Behavior

The series or DataFrame can be repr'd and printed and shows the data in a normal way.

Installed Versions

INSTALLED VERSIONS

commit : 37ea63d
python : 3.10.11.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.19044
machine : AMD64
processor : Intel64 Family 6 Model 78 Stepping 3, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : English_United States.1252

pandas : 2.0.1
numpy : 1.23.2
pytz : 2022.2.1
dateutil : 2.8.2
setuptools : 60.2.0
pip : 21.3.1
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 7.31.0
pandas_datareader: None
bs4 : 4.12.2
bottleneck : None
brotli :
fastparquet : None
fsspec : 2022.10.0
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 12.0.0
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
snappy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : 2.3.1
pyqt5 : None

[a-reich]

Awesome, thanks for your work on this!