TST (string dtype): resolve xfails in pandas/tests/apply + raise TypeError for ArrowArray accumulate
Resolve all remaining string xfails in `pandas/tests/apply`, except for one about cumsum not yet implemented for string dtype.

Also ensures we don't raise a pyarrow specific error in case of the pyarrow-backend for accumulation methods.

xref https://github.com/pandas-dev/pandas/issues/54792
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 fba5f08f048215a6e0a578f8bad7b7f2c9ee8eef
```

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

```
git commit -am 'Backport PR #60312: TST (string dtype): resolve xfails in pandas/tests/apply + raise TypeError for ArrowArray accumulate'
```

4. Push to a named branch:

```
git push YOURFORK 2.3.x:auto-backport-of-pr-60312-on-2.3.x
```

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

> "Backport PR #60312 on branch 2.3.x (TST (string dtype): resolve xfails in pandas/tests/apply + raise TypeError for ArrowArray accumulate)"

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).
                 Since you've got a ton going on I'm happy to take care of this backport Manual backport -> https://github.com/pandas-dev/pandas/pull/60328