BUG: pd.Series.replace(to_replace=...) does not preserve the original dtype of the series
- [X] I have checked that this issue has not already been reported.

- [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.

---
#### Code Sample, a copy-pastable example

```python
>>> s = pd.Series(["one", "two"], dtype="string")
>>> expected = pd.Series(["1", "2"], dtype="string")
>>> result = s.replace(to_replace={"one": "1", "two": "2"})
>>> expected
0    1
1    2
dtype: string
>>> result
0    1
1    2
dtype: object
```
#### Problem description

The `pandas.Series.replace` does not return a series with the same `dtype` as the the original series. This behaviour is produced only when the replace function is called using the argument `to_replace`.

Notice: Similar behaviour is produced with other dtypes as well, this issue is not limited to string dtype.

The investigation should probably start here: `/pandas/core/generic.py`

#### Expected Output
We would expect the `pandas.Series.replace(to_replace=...)` to preserve the dtype of the series.
In the above code sample, both of the series should have a dtype of string.
#### Output of ``pd.show_versions()``

<details>
<h2>INSTALLED VERSIONS</h2>
commit           : None
python           : 3.8.2.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 19.4.0
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : None
LANG             : None
LOCALE           : None.UTF-8

pandas           : 1.0.3
numpy            : 1.18.1
pytz             : 2019.3
dateutil         : 2.8.1
pip              : 20.0.2
setuptools       : 46.1.3.post20200330
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       : None
fastparquet      : None
gcsfs            : None
lxml.etree       : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pytables         : None
pytest           : None
pyxlsb           : None
s3fs             : None
scipy            : None
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
xlsxwriter       : None
numba            : None
</details>
