String dtype: disallow specifying the 'str' dtype with storage in [..] in string alias
The intention was for the new default `"str"` dtype to not include the storage in the string alias, and so to also not allow constructing it that way (this is discussed in the PDEP).

This is also implemented this way, as you can see when directly calling the extension dtype API:

```python
# for "string" this is allowed
>>> pd.StringDtype.construct_from_string("string[pyarrow]")
string[pyarrow]

# but for "str" not
>>> pd.StringDtype.construct_from_string("str[pyarrow]")
...
TypeError: Cannot construct a 'StringDtype' from 'str[pyarrow]'
```

However, when specifying this as a `dtype` argument in eg constructors (going through `pandas_dtype(...)`, which goes through the extension dtype registry), this "accidentally" kind of works, but gives an unexpected result:

```python
# this raises as expected
>>> pd.Series(["a"], dtype="str[python]")
TypeError: data type 'str[python]' not understood

# but this gives a result
>>> pd.Series(["a"], dtype="str[pyarrow]")
>>>
0    a
dtype: string[pyarrow]
>>> type(pd.Series(["a"], dtype="str[pyarrow]").dtype)
pandas.ArrowDtype
```

I think it is confusing that it does work in case of the pyarrow storage, but then does give a different dtype than what you would typically expect. 
So I would rather just disallow this case (which is what this PR does), although this is a small breaking change for people currently using `dtype="str[pyarrow]"` to get the ArrowDtype.
> I think it is confusing that it does work in case of the pyarrow storage, but then does give a different dtype than what you would typically expect. So I would rather just disallow this case (which is what this PR does), although this is a small breaking change for people currently using `dtype="str[pyarrow]"` to get the ArrowDtype.

This gives a definitively wrong result and so I think that puts it solidly in the bugfix camp, not a breaking change. 

 If we really cared we could convert that during the pickle read, although I dont think that would be a blocker. Generally using pickle to move from one environment to another is discouraged > If we really cared we could convert that during the pickle read, although I dont think that would be a blocker. Generally using pickle to move from one environment to another is discouraged

@WillAyd that comment about pickle was meant for the discussion in https://github.com/pandas-dev/pandas/issues/60639? Owee, I'm MrMeeseeks, Look at me.

There seem to be a conflict, please backport manually. Here are approximate instructions:

1. Checkout backport branch and update it.

```
git checkout 2.3.x
git pull
```

2. Cherry pick the first parent branch of the this PR on top of the older branch:
```
git cherry-pick -x -m1 7415aca37159a99f8f99d93a1908070ddf36178c
```

3. You will likely have some merge/cherry-pick conflict here, fix them and commit:

```
git commit -am "Backport PR #60661: String dtype: disallow specifying the 'str' dtype with storage in [..] in string alias"
```

4. Push to a named branch:

```
git push YOURFORK 2.3.x:auto-backport-of-pr-60661-on-2.3.x
```

5. Create a PR against branch 2.3.x, I would have named this PR:

> "Backport PR #60661 on branch 2.3.x (String dtype: disallow specifying the 'str' dtype with storage in [..] in string alias)"

And apply the correct labels and milestones.

Congratulations — you did some good work! Hopefully your backport PR will be tested by the continuous integration and merged soon!

Remember to remove the `Still Needs Manual Backport` label once the PR gets merged.

If these instructions are inaccurate, feel free to [suggest an improvement](https://github.com/MeeseeksBox/MeeseeksDev).
                 Manual backport -> https://github.com/pandas-dev/pandas/pull/60715 > @WillAyd that comment about pickle was meant for the discussion in #60639?

Ah...thanks for pointing that out