BUG: Unexpected behavior pandas.DataFrame.replace with "string" dtype
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- [x] I have confirmed this bug exists on the latest version of pandas.

- [x] (optional) I have confirmed this bug exists on the master branch of pandas.

---
I'm trying to remove certain characters in a DataFrame, in this case, I am trying to remove the **ñ**.
#### Code Sample

```python
df = pd.DataFrame([['añoos','asññ','ÑolÑÑss'],['añoos','asññ','ÑolÑÑss']], dtype='string')
df.replace({'ñ':'n',
            'Ñ':'N'}, 
           regex = True, inplace = True)
```
The output is:

|    | 0     | 1    | 2       |
|---:|:------|:-----|:--------|
|  0 | añoos | asññ | ÑolÑÑss |
|  1 | añoos | asññ | ÑolÑÑss |

#### Problem description

If I do not specify the dtype to ```string```, the output is the expected as follows:

#### Expected Output

```python
df = pd.DataFrame([['añoos','asññ','ÑolÑÑss'],['añoos','asññ','ÑolÑÑss']])
df.replace({'ñ':'n',
            'Ñ':'N'}, 
           regex = True, inplace = True)
print(df)
```


|    | 0     | 1    | 2       |
|---:|:------|:-----|:--------|
|  0 | anoos | asnn | NolNNss |
|  1 | anoos | asnn | NolNNss |
#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : 2cb96529396d93b46abab7bbc73a208e708c642e
python           : 3.8.5.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
Version          : 10.0.19041
machine          : AMD64
processor        : Intel64 Family 6 Model 158 Stepping 10, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : es_419.UTF-8
LOCALE           : Spanish_Colombia.1252

pandas           : 1.2.4
numpy            : 1.19.4
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 21.0.1
setuptools       : 54.2.0
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : 1.3.7
lxml.etree       : 4.6.2
html5lib         : None
pymysql          : 0.9.3
psycopg2         : 2.8.6 (dt dec pq3 ext lo64)
jinja2           : 2.11.3
IPython          : 7.22.0
pandas_datareader: None
bs4              : 4.6.0
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : 3.3.4
numexpr          : None
odfpy            : None
openpyxl         : 3.0.6
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : 1.5.1
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : 1.2.0
xlwt             : None
numba            : 0.52.0

</details>
