[BUG] singledispatch classmethods are not detected by MethodDocumenter

[picnixz]

Describe the bug

When using functools.singledispatchmethod together with classmethod, no :classmethod: directive option is added by sphinx.ext.autodoc.MethodDocumenter.

Using the example below, the reST directive result is

.. py:class:: MyClass()
   :module: class

   My class.


   .. py:method:: MyClass.dispatch(x)
      :module: class

      A singledispatch class method.


   .. py:method:: MyClass.method()
      :module: class
      :classmethod:

      A class method.

The issue lies in the following line:

sphinx/sphinx/ext/autodoc/__init__.py

Lines 2171 to 2172 in 669bcc0

	if inspect.isclassmethod(obj):
	self.add_line(' :classmethod:', sourcename)

The inspection of a classmethod when the latter is wrapped in a singledispatchmethod does not detect it as a classmethod. In particular, I would suggest replacing this test by the following line:

if inspect.isclassmethod(obj) or (
   inspect.is_singledispatch_method(obj)
   and inspect.isclassmethod(obj.func)
):
   ...

How to Reproduce

class.py

from functools import singledispatchmethod

class MyClass:
    """My class."""

    @singledispatchmethod  
    @classmethod
    def dispatch(cls, x):
      """A singledispatch class method."""
      return 0

    @classmethod
    def method(cls):
        """A class method."""
        pass

index.rst

Foo
===

.. autoclass:: class.MyClass
   :members:

conf.py

import os
import sys

sys.path.insert(0, os.path.abspath('.'))

project = 'Foo'
copyright = '2023, picnixz'
author = 'picnixz'

extensions = ['sphinx.ext.autodoc']

templates_path = ['_templates']

master_doc = 'index'

include_patterns = ['index.rst', 'class.py']
exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store']

html_theme = 'alabaster'
html_static_path = ['_static']

Environment Information

Platform:              linux; (Linux-5.3.18-lp152.106-default-x86_64-with-glibc2.26)
Python version:        3.10.3 (main, Jan 31 2023, 10:47:25) [GCC 7.5.0])
Python implementation: CPython
Sphinx version:        6.1.3
Docutils version:      0.18.1
Jinja2 version:        3.1.2
Pygments version:      2.14.0

Sphinx extensions

['sphinx.ext.autodoc']

Additional context

The same issue seems to happen with staticmethod: #10529 (comment)