BUG: pd.Series.argsort misaligned index
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- [X] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

Code:
```python
series = pd.Series([30, 10, 20], index=['c', 'a', 'b'])
order = series.argsort()
order
```
Output:
```
c    1
a    2
b    0
dtype: int64
```

#### Problem description

It appears that the argsort output str index order (c, a, b) remains the same as the input data, while the numeric indices (1, 2, 0) are referring to the input data in a different order. This means the str index no longer corresponds with the values (the numeric indices) in the resulting Series. This behavior is confusing, since it sort of looks like c would be the 1st element (0-indexed), a the 2nd, and b the 0th, which is incorrect.

There's actually another example of this here: https://www.geeksforgeeks.org/python-pandas-series-argsort/. The str indices in the result of the argsort don't give any useful information - only the order of the numeric indices is relevant.

#### Expected Output

I'm not sure if it would make more sense if str indices were reordered to match the numeric indices, like this:
```
a    1
b    2
c    0
dtype: int64
```
This might be nice, for example, to get the indices of the largest N elements: `order.index[-N:]`. The common workflow `series[series.argsort()]` still seems to work, but I'm not sure of all the other indexing implications.

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : 2cb96529396d93b46abab7bbc73a208e708c642e
python           : 3.7.5.final.0
python-bits      : 64
OS               : Linux
OS-release       : 3.10.0-1160.25.1.el7.x86_64
Version          : #1 SMP Tue Apr 13 18:55:45 EDT 2021
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : C.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.2.4
numpy            : 1.18.5
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 21.1
setuptools       : 56.0.0
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 2.11.3
IPython          : 7.22.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : 3.4.1
numexpr          : None
odfpy            : None
openpyxl         : 3.0.7
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : 1.6.3
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : 0.53.1

</details>
