`singledispatchmethod` inspected signature incorrectly includes `self`

Bug report

Bug description:

The result of singledispatchmethod.__get__ is wrapped to imitate the underlying function, instead of the result of func.__get__. This leads to an incorrect signature being reported by inspect.signature, which includes the leading self argument, thus misleading introspection tools as to the real arguments the method accepts.

import inspect
from functools import singledispatchmethod

class A:
    @singledispatchmethod
    def a(self, arg):
        pass

sig = inspect.signature(A().a)
# <Signature (self, arg)> but we expect <Signature (arg)>

sig.bind(None)  # should be OK because `A().a(None)` is OK. Instead:
# TypeError: missing a required argument: 'arg'
# because the first argument is erroneously bound to `self`.

One way to fix this might be to edit https://github.com/python/cpython/blob/6258844c27e3b5a43816e7c559089a5fe0a47123/Lib/functools.py#L979 to read instead

update_wrapper(_method, self.func.__get__(obj, cls))

CPython versions tested on:

3.10, 3.12

Operating systems tested on:

Linux, Windows

Read Lib/functools.py around line 979, focusing on how singledispatchmethod.get wraps the bound method. Run the provided inspect.signature and sig.bind reproduction; done means the bound signature omits self, accepts the method's actual argument, and the relevant tests pass.