functools.singledispatch registration prioritizes the types of normal arguments before positional-only ones

Bug report

Bug description:

Decorator-based functools.singledispatch registration prioritizes the types of normal arguments before positional-only ones when getting "the type of the first argument".

This means that a function of def f(pos: str, /, other: int) will be registered to be dispatched for other's type (int) instead of pos (str).

To reproduce:

import functools

@functools.singledispatch
def f(arg, /, extra):
    return f"{arg}: undispatched type"

@f.register
def f_int(arg: int, /, extra: str):
    return f"{arg} is a {type(arg)} (dispatched by int)"

@f.register
def f_str(arg: str, /, extra: int):
    return f"{arg} is a {type(arg)} (dispatched by str)"

print(f(None, "extra"))
print(f(1, "extra"))
print(f("s", "extra"))

Result:

None: undispatched type
1 is a <class 'int'> (dispatched by str)
s is a <class 'str'> (dispatched by int)

Expected:

None: undispatched type
1 is a <class 'int'> (dispatched by int)
s is a <class 'str'> (dispatched by str)

CPython versions tested on:

3.9, 3.10, 3.11, 3.12, 3.13, 3.14, CPython main branch

Operating systems tested on:

macOS

Linked PRs

• gh-143888
• gh-143465

Start from the functools.singledispatch registration path and reproduce the example with positional-only and normal arguments. Done means registration selects the first positional-only argument's type and the shown dispatch results match the expected output, with regression coverage added and the relevant tests passing.