BUG: 'assign' on empty DataFrame with dtype=string column gives "ValueError: StringArray requires a sequence of strings or pandas.NA"
- [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.

---

**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

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

```python
import pandas as pd
pd.show_versions()

broken = pd.DataFrame([], columns=["a"], dtype="string")
broken.assign(b=[1]) # ValueError: StringArray requires a sequence of strings or pandas.NA

working1 = pd.DataFrame([pd.NA], columns=["a"], dtype="string")
working1.assign(b=[1]) # 0  <NA>  1
working2 = pd.DataFrame([], columns=["a"], dtype="object")
working2.assign(b=[1]) # 0  NaN  1
```

Full traceback:

```
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File ".../site-packages/pandas/core/frame.py", line 4481, in assign
    data[k] = com.apply_if_callable(v, data)
  File ".../site-packages/pandas/core/frame.py", line 3607, in __setitem__
    self._set_item(key, value)
  File ".../site-packages/pandas/core/frame.py", line 3779, in _set_item
    value = self._sanitize_column(value)
  File ".../site-packages/pandas/core/frame.py", line 4497, in _sanitize_column
    self._ensure_valid_index(value)
  File ".../site-packages/pandas/core/frame.py", line 3853, in _ensure_valid_index
    self._mgr = self._mgr.reindex_axis(index_copy, axis=1, fill_value=np.nan)
  File ".../site-packages/pandas/core/internals/base.py", line 89, in reindex_axis
    return self.reindex_indexer(
  File ".../site-packages/pandas/core/internals/managers.py", line 680, in reindex_indexer
    new_blocks = [
  File ".../site-packages/pandas/core/internals/managers.py", line 681, in <listcomp>
    blk.take_nd(
  File ".../site-packages/pandas/core/internals/blocks.py", line 1512, in take_nd
    new_values = self.values.take(indexer, fill_value=fill_value, allow_fill=True)
  File ".../site-packages/pandas/core/arrays/_mixins.py", line 108, in take
    return self._from_backing_data(new_data)
  File ".../site-packages/pandas/core/arrays/numpy_.py", line 118, in _from_backing_data
    return type(self)(arr)
  File ".../site-packages/pandas/core/arrays/string_.py", line 318, in __init__
    self._validate()
  File ".../site-packages/pandas/core/arrays/string_.py", line 323, in _validate
    raise ValueError("StringArray requires a sequence of strings or pandas.NA")
ValueError: StringArray requires a sequence of strings or pandas.NA
```

#### Problem description

The `broken` code doesn't seem meaningfully different to the working versions, but throws an exception; from a very quick look (and as hinted by the `working2` output), it looks like the `StringArray` is being constructed with an array containing NaN/`float('nan')`, and that value is considered/treated different to `pd.NA`.

There's a few other issues mentioning this error, but it wasn't obvious to me if they're the same:

- #40800
- #40823
- #40824

#### Expected Output

The `broken` code should behave similarly to the very similar `working1` and `working2`. The output should be the same as the `working1`:

```
      a  b
0  <NA>  1
```

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

<details>

INSTALLED VERSIONS
------------------
commit           : 5f648bf1706dd75a9ca0d29f26eadfbb595fe52b
python           : 3.8.7.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 20.5.0
Version          : Darwin Kernel Version 20.5.0: Sat May  8 05:10:31 PDT 2021; root:xnu-7195.121.3~9/RELEASE_ARM64_T8101
machine          : arm64
processor        : arm
byteorder        : little
LC_ALL           : None
LANG             : en_AU.UTF-8
LOCALE           : en_AU.UTF-8

pandas           : 1.3.2
numpy            : 1.20.2
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 21.2.4
setuptools       : 49.2.1
Cython           : None
pytest           : 6.1.2
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : 2.9.1 (dt dec pq3 ext lo64)
jinja2           : 2.11.3
IPython          : 7.22.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : 3.0.7
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : 1.7.1
sqlalchemy       : 1.3.20
tables           : None
tabulate         : 0.8.9
xarray           : None
xlrd             : 2.0.1
xlwt             : 1.3.0
numba            : None

</details>
