BUG: DataFrame.sort_index is failing when axis='columns' and ignore_index=True

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

In [3]: pdf
Out[3]: 
      b  a  1  e  d
0   1.0  1  a  3  1
1   3.0  4  b  1  2
2  <NA>  3  c  4  8

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

In [5]: df.sort_index(axis='columns', ignore_index=True)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[5], line 1
----> 1 df.sort_index(axis='columns', ignore_index=True)

File /nvme/0/pgali/envs/cudfdev/lib/python3.10/site-packages/pandas/core/frame.py:7134, in DataFrame.sort_index(self, axis, level, ascending, inplace, kind, na_position, sort_remaining, ignore_index, key)
   7037 def sort_index(
   7038     self,
   7039     *,
   (...)
   7048     key: IndexKeyFunc | None = None,
   7049 ) -> DataFrame | None:
   7050     """
   7051     Sort object by labels (along an axis).
   7052 
   (...)
   7132     d  4
   7133     """
-> 7134     return super().sort_index(
   7135         axis=axis,
   7136         level=level,
   7137         ascending=ascending,
   7138         inplace=inplace,
   7139         kind=kind,
   7140         na_position=na_position,
   7141         sort_remaining=sort_remaining,
   7142         ignore_index=ignore_index,
   7143         key=key,
   7144     )

File /nvme/0/pgali/envs/cudfdev/lib/python3.10/site-packages/pandas/core/generic.py:5257, in NDFrame.sort_index(self, axis, level, ascending, inplace, kind, na_position, sort_remaining, ignore_index, key)
   5255 if ignore_index:
   5256     axis = 1 if isinstance(self, ABCDataFrame) else 0
-> 5257     new_data.set_axis(axis, default_index(len(indexer)))
   5259 result = self._constructor_from_mgr(new_data, axes=new_data.axes)
   5261 if inplace:

File /nvme/0/pgali/envs/cudfdev/lib/python3.10/site-packages/pandas/core/internals/managers.py:227, in BaseBlockManager.set_axis(self, axis, new_labels)
    225 def set_axis(self, axis: AxisInt, new_labels: Index) -> None:
    226     # Caller is responsible for ensuring we have an Index object.
--> 227     self._validate_set_axis(axis, new_labels)
    228     self.axes[axis] = new_labels

File /nvme/0/pgali/envs/cudfdev/lib/python3.10/site-packages/pandas/core/internals/base.py:85, in DataManager._validate_set_axis(self, axis, new_labels)
     82     pass
     84 elif new_len != old_len:
---> 85     raise ValueError(
     86         f"Length mismatch: Expected axis has {old_len} elements, new "
     87         f"values have {new_len} elements"
     88     )

ValueError: Length mismatch: Expected axis has 3 elements, new values have 2 elements

Issue Description

When we try to sort a dataframe by columns and pass ignore_index=True, there is a failure.

Expected Behavior

I expect it to not fail and return a dataframe with existing columns/dropped columns with labels 0, 1, 2...n-1.

Installed Versions

In [6]: pd.show_versions()
INSTALLED VERSIONS

commit : a671b5a
python : 3.10.13.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.0-88-generic
Version : #98-Ubuntu SMP Mon Oct 2 15:18:56 UTC 2023
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.1.4
numpy : 1.24.4
pytz : 2023.3.post1
dateutil : 2.8.2
setuptools : 68.2.2
pip : 23.3.1
Cython : 3.0.6
pytest : 7.4.3
hypothesis : 6.91.0
sphinx : 7.2.6
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.18.1
pandas_datareader : None
bs4 : 4.12.2
bottleneck : None
dataframe-api-compat: None
fastparquet : None
fsspec : 2023.12.1
gcsfs : None
matplotlib : None
numba : 0.57.1
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 14.0.1
pyreadstat : None
pyxlsb : None
s3fs : 2023.12.1
scipy : 1.11.4
sqlalchemy : 2.0.23
tables : None
tabulate : 0.9.0
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None