BUG: validity of interchange column is incorrectly set to Some for 'large-string[pyarrow]'

[MarcoGorelli]

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

df = pd.DataFrame({"a": ["x"]}, dtype="large_string[pyarrow]")
print(df.__dataframe__().get_column_by_name('a').get_buffers())
print(df['a'].array._pa_array.chunks[0].buffers())

Issue Description

this outputs

{'data': (PandasBuffer({'bufsize': 1, 'ptr': 140384569941504, 'device': 'CPU'}), (<DtypeKind.UINT: 1>, 8, 'C', '=')), 'validity': (PandasBuffer({'bufsize': 1, 'ptr': 94849242700288, 'device': 'CPU'}), (<DtypeKind.BOOL: 20>, 8, 'b', '=')), 'offsets': (PandasBuffer({'bufsize': 16, 'ptr': 94849235835952, 'device': 'CPU'}), (<DtypeKind.INT: 0>, 64, 'l', '='))}
[None, <pyarrow.Buffer address=0x7fadd6808000 size=16 is_cpu=True is_mutable=True>, <pyarrow.Buffer address=0x7fadd6808080 size=1 is_cpu=True is_mutable=True>]

Expected Behavior

{'data': (PandasBuffer({'bufsize': 1, 'ptr': 140384569941504, 'device': 'CPU'}), (<DtypeKind.UINT: 1>, 8, 'C', '=')), 'validity': None, 'offsets': (PandasBuffer({'bufsize': 16, 'ptr': 94849235835952, 'device': 'CPU'}), (<DtypeKind.INT: 0>, 64, 'l', '='))}
[None, <pyarrow.Buffer address=0x7fadd6808000 size=16 is_cpu=True is_mutable=True>, <pyarrow.Buffer address=0x7fadd6808080 size=1 is_cpu=True is_mutable=True>]

Installed Versions

INSTALLED VERSIONS

commit : b033ca9
python : 3.10.12.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.146.1-microsoft-standard-WSL2
Version : #1 SMP Thu Jan 11 04:09:03 UTC 2024
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : C.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.1.0.dev0+761.gb033ca94e7
numpy : 1.26.4
pytz : 2024.1
dateutil : 2.8.2
setuptools : 69.1.1
pip : 24.0
Cython : 3.0.8
pytest : 8.0.2
hypothesis : 6.98.15
sphinx : 7.2.6
blosc : None
feather : None
xlsxwriter : 3.2.0
lxml.etree : 5.1.0
html5lib : 1.1
pymysql : 1.4.6
psycopg2 : 2.9.9
jinja2 : 3.1.3
IPython : 8.22.1
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.3
bottleneck : 1.3.8
fastparquet : 2024.2.0
fsspec : 2024.2.0
gcsfs : 2024.2.0
matplotlib : 3.8.3
numba : 0.59.0
numexpr : 2.9.0
odfpy : None
openpyxl : 3.1.2
pyarrow : 15.0.0
pyreadstat : 1.2.6
python-calamine : None
pyxlsb : 1.0.10
s3fs : 2024.2.0
scipy : 1.12.0
sqlalchemy : 2.0.27
tables : 3.9.2
tabulate : 0.9.0
xarray : 2024.2.0
xlrd : 2.0.1
zstandard : 0.22.0
tzdata : 2024.1
qtpy : 2.4.1
pyqt5 : None