BUG: Outer merge casts EA dtype to object 
- [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.

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

---

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

```python
d1 = pd.DataFrame([("a",)], columns=["id"], dtype="string")
d2 = pd.DataFrame([("b",)], columns=["id"], dtype="string")
result = d1.merge(d2, on="id", how="outer")
dtype = result.dtypes["id"]
print(dtype) # expected 'string', but is 'object'
```

#### Problem description

When doing an outer merge on a column of type `string`, the result contains this column with the type `object`. This makes it more difficult to use the new `string` type.

The problem doesn't occur with the types `Int32`, `Float32`, `boolean`. It seems to be specific to the `string` type.

The problem doesn't occur with a left, right or inner-merge.

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : 7d32926db8f7541c356066dcadabf854487738de
python           : 3.7.3.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 18.7.0
Version          : Darwin Kernel Version 18.7.0: Tue Nov 10 00:07:31 PST 2020; root:xnu-4903.278.51~1/RELEASE_X86_64
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : en_US.UTF-8
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.2.2
numpy            : 1.20.1
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 20.2.4
setuptools       : 52.0.0.post20210125
Cython           : None
pytest           : 6.0.1
hypothesis       : 5.30.1
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 2.11.3
IPython          : 7.20.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : None
sqlalchemy       : 1.3.23
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : None

</details>
