PERF: Series.str.get for pyarrow-backed strings
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [x] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [x] Added an entry in the latest `doc/source/whatsnew/v2.1.0.rst` file if fixing a bug or adding a new feature.

```
import pandas as pd
import pandas._testing as tm
import pyarrow as pa

N = 1_000_000

ser = pd.Series(tm.makeStringIndex(N), dtype=pd.ArrowDtype(pa.string()))

%timeit ser.str.get(1)

# 70.1 ms ± 3.13 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)  -> main
# 37.7 ms ± 2.09 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)  -> PR
```
```
sort whatsnew entries alphabetically....................................................................Failed
- hook id: sort-whatsnew-items
- duration: 0.04s
- exit code: 1
- files were modified by this hook
pre-commit hook(s) made changes.
If you are seeing this message in CI, reproduce locally with: `pre-commit run --all-files`.
To run `pre-commit` as part of git workflow, use `pre-commit install`.
All changes made by hooks:
diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index 44ba2ac..a7ad001 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -290,10 +290,10 @@ Performance improvements
 - Performance improvement in :meth:`.DataFrameGroupBy.groups` (:issue:`53088`)
 - Performance improvement in :meth:`DataFrame.loc` when selecting rows and columns (:issue:`53014`)
 - Performance improvement in :meth:`Series.corr` and :meth:`Series.cov` for extension dtypes (:issue:`52502`)
+- Performance improvement in :meth:`Series.str.get` for pyarrow-backed strings (:issue:`53152`)
 - Performance improvement in :meth:`Series.to_numpy` when dtype is a numpy float dtype and ``na_value`` is ``np.nan`` (:issue:`52430`)
 - Performance improvement in :meth:`~arrays.ArrowExtensionArray.to_numpy` (:issue:`52525`)
 - Performance improvement when doing various reshaping operations on :class:`arrays.IntegerArrays` & :class:`arrays.FloatingArray` by avoiding doing unnecessary validation (:issue:`53013`)
-- Performance improvement in :meth:`Series.str.get` for pyarrow-backed strings (:issue:`53152`)
 -
``` Thanks @lukemanley 