BUG: DataFrame.replace with regex on StringDtype column with NA values stops replacing after first NA

[Timost]

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
df = pd.DataFrame({'old': ['my', 'test', pd.NA, 'word', 'to', 'replace']}, dtype="string")
# In [3]: df
# Out[3]:
#        old
# 0       my
# 1     test
# 2     <NA>
# 3     word
# 4       to     
# 5  replace

 df['old'].replace(regex={r't.*': 'replaced'})
# Out[4]:
# 0          my
# 1    replaced
# 2        <NA>
# 3        word
# 4          to    <---- *** should have replaced this one ***
# 5     replace
# Name: old, dtype: string

df['old'].astype('object').replace(regex={r't.*': 'replaced'})
# Out[5]:
# 0          my
# 1    replaced
# 2        <NA>
# 3        word
# 4    replaced  <---- *** properly replaced***
# 5     replace
# Name: old, dtype: object

Issue Description

Hi, thank you for pandas ❤🙏

When using regex, pandas.DataFrame.replace on a StringDtype column containing pd.NA values, the replacement stops after the first pd.NA value is met.

The problem doesn't occur when using the object dtype.

Expected Behavior

I would expect the replacement to ignore NA values and still replace all matching values for both the object and the StringDtype dtypes.

Installed Versions

INSTALLED VERSIONS

commit : a671b5a
python : 3.11.5.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.133.1-microsoft-standard-WSL2
Version : #1 SMP Thu Oct 5 21:02:42 UTC 2023
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : C.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.1.4
numpy : 1.26.2
pytz : 2023.3.post1
dateutil : 2.8.2
setuptools : 69.0.2
pip : 23.3.1
Cython : None
pytest : 7.4.3
hypothesis : None
sphinx : 7.2.6
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.18.1
pandas_datareader : None
bs4 : 4.12.2
bottleneck : None
dataframe-api-compat: None
fastparquet : None
fsspec : 2023.12.2
gcsfs : None
matplotlib : 3.8.2
numba : None
numexpr : None
odfpy : None
openpyxl : 3.1.2
pandas_gbq : None
pyarrow : 10.0.1
pyreadstat : None
pyxlsb : None
s3fs : 2023.12.2
scipy : 1.11.4
sqlalchemy : 2.0.23
tables : None
tabulate : 0.9.0
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None

[rootsmusic]

Oops, pasting again. Maybe related to issue #54399

[Timost]

Thank you for fixing this !