API: More permissive conversion to StringDtype
- [x] closes #31204
- [ ] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [ ] whatsnew entry

This is a proposal to make using ``StringDtype`` more permissive and be usable inplace of ``dtype=str``.

ATM converting to StringDtype will only accept arrays that are ``str`` already, meaning you will often have to use ``astype(str).astype("string")`` to be sure not to get errors, which can be tedious. For example these fail in master and work in this PR:

```python
>>> pd.Series([1,2, np.nan], dtype="string")
0       1
1       2
2    <NA>
dtype: string
>>> pd.array([1,2, np.nan], dtype="string")
<StringArray>
['1', '2', <NA>]
Length: 3, dtype: string
>>> pd.Series([1,2, np.nan]).astype("string")
0     1.0
1     2.0
2    <NA>
dtype: string
>>> pd.Series([1,2, np.nan], dtype="Int64").astype("string")
0       1
1       2
2    <NA>
dtype: string
```

etc. now work. Previously the above all gave errors.

Obviously tests and doc updates are still missing, but I would appreciate feedback if this solution looks ok.