TST (string dtype): resolve all infer_string TODO/xfails in pandas/tests/arrays
Together with the test changes in https://github.com/pandas-dev/pandas/pull/59678 and https://github.com/pandas-dev/pandas/pull/59682, this PR then resolves the remaining `infer_string` TODO or xfails in `pandas/tests/arrays`

xref https://github.com/pandas-dev/pandas/issues/54792/
This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. 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 4f328f08df90906198b3a3f955ab321018964f0a
```

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

```
git commit -am 'Backport PR #59686: TST (string dtype): resolve all infer_string TODO/xfails in pandas/tests/arrays'
```

4. Push to a named branch:

```
git push YOURFORK 2.3.x:auto-backport-of-pr-59686-on-2.3.x
```

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

> "Backport PR #59686 on branch 2.3.x (TST (string dtype): resolve all infer_string TODO/xfails in pandas/tests/arrays)"

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/60020