BUG: sort_index not preserving index when ascending=False

[galipremsagar]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

In [1]: import pandas as pd

In [2]: import numpy as np

In [3]: pdf = pd.DataFrame(
   ...:         {
   ...:             "b": [1.0, 3.0, np.nan],
   ...:             "a": [1, 4, 3],
   ...:             1: ["a", "b", "c"],
   ...:             "e": [3, 1, 4],
   ...:             "d": [1, 2, 8],
   ...:         }
   ...:     )

In [4]: pdf = pdf.set_index(["b", "a", 1])

In [5]: pdf.sort_index(axis='columns')
Out[5]: 
         d  e
b   a 1      
1.0 1 a  1  3
3.0 4 b  2  1
NaN 3 c  8  4

In [6]: pdf.sort_index(axis='columns', ignore_index=True)
Out[6]: 
         0  1
b   a 1      
1.0 1 a  1  3
3.0 4 b  2  1
NaN 3 c  8  4

In [7]: pdf.sort_index(axis='columns', ignore_index=True, ascending=True)
Out[7]: 
         0  1
b   a 1      
1.0 1 a  1  3
3.0 4 b  2  1
NaN 3 c  8  4

In [8]: pdf.sort_index(axis='columns', ignore_index=True, ascending=False)
Out[8]: 
   e  d
0  3  1
1  1  2
2  4  8

In [9]: pd.__version__
Out[9]: '2.2.0'

Issue Description

When ascending=False the index is being dropped.

Expected Behavior

Not dropping index.

Installed Versions

INSTALLED VERSIONS

commit : fd3f571
python : 3.10.13.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.0-91-generic
Version : #101-Ubuntu SMP Tue Nov 14 13:30:08 UTC 2023
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.0
numpy : 1.26.3
pytz : 2024.1
dateutil : 2.8.2
setuptools : 69.0.3
pip : 24.0
Cython : 3.0.8
pytest : 7.4.4
hypothesis : 6.98.1
sphinx : 6.2.1
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.3
IPython : 8.21.0
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.3
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : 2024.2.0
gcsfs : None
matplotlib : None
numba : 0.59.0
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 14.0.1
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : 2024.2.0
scipy : 1.12.0
sqlalchemy : 2.0.25
tables : None
tabulate : 0.9.0
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.4
qtpy : None
pyqt5 : None

[galipremsagar]

cc: @mroeschke

[mroeschke]

For clarity, Out[6]: and Out[7]: are incorrect, the resulting index should match Out[8]

Nevermind, I realized ignore_index=True applies to the "columns" here