BUG: `pd.api.types.is_string_dtype()` returns inconsistent results for Categorical series vs dtype

[nsarang]

Pandas version checks

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Reproducible Example

import pandas as pd

series = pd.Categorical(['A', 'B', 'C'])
print(f"is_string_dtype(series): {pd.api.types.is_string_dtype(series)}") # True  
print(f"is_string_dtype(series.dtype): {pd.api.types.is_string_dtype(series.dtype)}") # False

Issue Description

pd.api.types.is_string_dtype() returns inconsistent results when passed a Categorical series directly versus the dtype of that series.

Expected Behavior

IMO, both calls should return False since a Categorical is not a string dtype.

Installed Versions

INSTALLED VERSIONS

commit : c888af6
python : 3.11.0
python-bits : 64
OS : Darwin
OS-release : 24.3.0
Version : Darwin Kernel Version 24.3.0: Thu Jan 2 20:24:23 PST 2025; root:xnu-11215.81.4~3/RELEASE_ARM64_T8122
machine : arm64
processor : arm
byteorder : little
LC_ALL : None
LANG : None
LOCALE : None.UTF-8

pandas : 2.3.1
numpy : 2.3.1
pytz : 2025.2
dateutil : 2.9.0.post0
pip : 25.0.1
Cython : None
sphinx : None
IPython : 9.4.0
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.13.4
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : 2025.3.0
html5lib : None
hypothesis : 6.138.0
gcsfs : 2025.3.0
jinja2 : 3.1.6
lxml.etree : None
matplotlib : 3.10.1
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 19.0.1
pyreadstat : None
pytest : 8.3.5
python-calamine : None
pyxlsb : None
s3fs : 2025.3.0
scipy : 1.15.2
sqlalchemy : 2.0.39
tables : None
tabulate : 0.9.0
xarray : 2025.6.1
xlrd : None
xlsxwriter : None
zstandard : None
tzdata : 2025.2
qtpy : None
pyqt5 : None