Converting a StringDtype series to an Inte64Dtype not working as expected
I am interested in converting a StringDtype series to an Inte64Dtype. The following code produces a TypeError:

```
x = pd.Series(['1', pd.NA, '3'], dtype=pd.StringDtype())
x.astype('Int64')
...
TypeError: data type not understood
```


If I rewrite it as follows, I get a different TypeError:

```
x = pd.Series(['1', pd.NA, '3'], dtype=pd.StringDtype())
x.astype(int)
...
TypeError: int() argument must be a string, a bytes-like object or a number, not 'NAType
```


The only way I have been able to convert from StringDtype is:

```
x = pd.Series(['1', pd.NA, '3'], dtype=pd.StringDtype())
pd.to_numeric(x, errors='coerce').convert_dtypes()
...
0       1
1    <NA>
2       3
dtype: Int64
```

This works fine, but is inelegant. I would have expect astype to be able to do the conversion directly. Is there a recommended way to convert between these types?