Improve the register_index_accessor Documentation
- [x] closes #49202 
- [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/vX.X.X.rst` file if fixing a bug or adding a new feature.

@mroeschke  Some doc checks are failing, here is the issue... 
_register_accessor has it's own docs, which are appearing for all of 3 index, series and dataframe accessor.
Now that I've put in the correct docs of this function.. the old docs are still being injected apart from the new docs.

How to remove this issue ? .. My guess is to remove the decorator itself for this `_register_index_accessor` method.

What should be the correct way to fix the error? @phofl The CI is all clean now, and I think PR is ready for another round of review . > Can you post a screenshot on how this looks?

I'm trying [official pandas](https://pandas.pydata.org/docs/development/contributing_documentation.html) guide to build docs locally. but I'm getting following error

```
(pytorch) anshuu@monuu:~/Desktop/os/pandas/doc$ python make.py clean
Traceback (most recent call last):
  File "make.py", line 377, in <module>
    sys.exit(main())
  File "make.py", line 359, in main
    globals()["pandas"] = importlib.import_module("pandas")
  File "/home/anshuu/anaconda3/envs/pytorch/lib/python3.8/importlib/__init__.py", line 127, in import_module
    return _bootstrap._gcd_import(name[level:], package, level)
  File "<frozen importlib._bootstrap>", line 1014, in _gcd_import
  File "<frozen importlib._bootstrap>", line 991, in _find_and_load
  File "<frozen importlib._bootstrap>", line 975, in _find_and_load_unlocked
  File "<frozen importlib._bootstrap>", line 671, in _load_unlocked
  File "<frozen importlib._bootstrap_external>", line 843, in exec_module
  File "<frozen importlib._bootstrap>", line 219, in _call_with_frames_removed
  File "/home/anshuu/Desktop/os/pandas/pandas/__init__.py", line 22, in <module>
    from pandas.compat import is_numpy_dev as _is_numpy_dev  # pyright: ignore # noqa:F401
  File "/home/anshuu/Desktop/os/pandas/pandas/compat/__init__.py", line 18, in <module>
    from pandas.compat.numpy import (
  File "/home/anshuu/Desktop/os/pandas/pandas/compat/numpy/__init__.py", line 4, in <module>
    from pandas.util.version import Version
  File "/home/anshuu/Desktop/os/pandas/pandas/util/__init__.py", line 2, in <module>
    from pandas.util._decorators import (  # noqa:F401
  File "/home/anshuu/Desktop/os/pandas/pandas/util/_decorators.py", line 14, in <module>
    from pandas._libs.properties import cache_readonly
  File "/home/anshuu/Desktop/os/pandas/pandas/_libs/__init__.py", line 13, in <module>
    from pandas._libs.interval import Interval
ModuleNotFoundError: No module named 'pandas._libs.interval'

``` Can you rebuild our extensions? > Can you rebuild our extensions?

how to rebuilding extensions ? 

I tried reinstalling anaconda, as well as just python in windows machine, facing the same issue @phofl 
python version 3.8.10 https://pandas.pydata.org/docs/development/contributing_environment.html

The first note about building the c extensions ![image](https://user-images.githubusercontent.com/51750587/199228024-0f1e8a9d-dba1-4e20-8184-51933e869e4d.png)

@phofl  Docker is amazing, managed to pull it and build documentation. Here is how it looks like  Is this PR ready to merge @phofl ? @mroeschke @jbrockmendel @phofl could you please review this PR and give feedback?
 This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. Thanks for the pull request, but it appears to have gone stale. If interested in continuing, please merge in the main branch, address any review comments and/or failing tests, and we can reopen.