BUG: add_categories does not honour pd.StringDtype of new categories (and downcasts to object instead)

[bollard]

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


c = pd.Categorical(pd.Series(["a", "b", "a"], dtype=pd.StringDtype()))
c.add_categories(pd.Series(["c", "d"], dtype=pd.StringDtype())).categories.dtype
>>> dtype('O')

Issue Description

Hi,

I've noticed that when adding two different pd.Categorical objects (whose .categories.dtype == pd.StringDtype()), add_categories will downcast back to object.

Interestingly, this doesn't seem to happen with, for example, pd.Int64Dtype():

d = pd.Categorical(pd.Series([1, 2, 1], dtype=pd.Int64Dtype()))
d.add_categories(pd.Series([3, 4], dtype=pd.Int64Dtype())).categories.dtype
>>> dtype('int64')

Thanks

Expected Behavior

import pandas as pd


c = pd.Categorical(pd.Series(["a", "b", "a"], dtype=pd.StringDtype()))
c.add_categories(pd.Series(["c", "d"], dtype=pd.StringDtype())).categories.dtype
>>> string[python]

Installed Versions

INSTALLED VERSIONS

commit : 87cfe4e
python : 3.10.4.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.19044
machine : AMD64
processor : Intel64 Family 6 Model 165 Stepping 3, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : English_United Kingdom.1252

pandas : 1.5.0
numpy : 1.23.1
pytz : 2022.1
dateutil : 2.8.2
setuptools : 63.4.1
pip : 22.1.2
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader: None
bs4 : None
bottleneck : 1.3.5
brotli : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : 2.8.3
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
snappy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
zstandard : None
tzdata : None

[bollard]

Have also just noticed similar behaviour with rename_categories

c = pd.Categorical(pd.Series(["a", "b", "a"], dtype=pd.StringDtype()))
c.rename_categories({"a": "z"}).categories.dtype
>>> dtype('O')

Here I can understand the downcast if I passed, say {"a": 1}, but I would have hoped that as "z" is compatible with pd.StringDtype() a downcast wouldn't be necessary. Again pd.Int64Dtype doesn't seem to be affected:

c = pd.Categorical(pd.Series([1, 2, 1], dtype=pd.Int64Dtype()))
c.rename_categories({1: 10}).categories.dtype
>>> dtype('int64')

[phofl]

Hi, thanks for your report. This does not work for "Int64". The correct result would be dtype("Int64")

[bollard]

Ah yes of course it is. Apologies, staring at this for too long but clearly still not looking closely enough