Wrong Signature for singledispatch'ed functions/methods

An example:

$ cat -n spam.py 
     1  from __future__ import annotations
     2  from functools import singledispatch
     3  
     4  @singledispatch
     5  def foo(x: int) -> int:
     6      return x + 1
     7  
     8  @foo.register
     9  def _(x: str) -> str:
    10      return "Hello, " + x
$ python
Python 3.11.1+ (heads/3.11:ba88628808, Jan 14 2023, 08:40:06) [GCC 10.2.1 20210110] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import inspect, spam
>>> inspect.signature(spam.foo)
<Signature (x: 'int') -> 'int'>

I would expect here something like <Signature (x: int | str) -> int | str> (i.e. union of types for returned value, same for argument) or an exception.

I'm not sure that the first option is on the table: more accurately this situation fits to case of multiple function signatures (like we have in the stdlib e.g. for the min/max). But the current signature() output is misleading.

UPD: In fact, the Signature must be like <Signature (x: int | str, /) -> int | str>, because:

>>> spam.foo(x=1)
Traceback (most recent call last):
  ...
TypeError: foo requires at least 1 positional argument

Or we can make singledispatch'ed function to be with a positional-only argument iff argument names for different overloaded implementations are different.

PS: Inspired by https://discuss.python.org/t/signatures-a-call-to-action/23580

Reproduziere das Beispiel mit functools.singledispatch und inspect.signature, einschließlich des im Bericht gezeigten Verhaltens bei Positionsargumenten. Entscheide, welche Signatursemantik beabsichtigt ist, und füge dann eine Regressionstestabdeckung hinzu, die das vereinbarte Ergebnis demonstriert; das Issue ist abgeschlossen, wenn singledispatch-Signaturen nicht mehr irreführend nur die Basisimplementierung darstellen.