self is never positional-only unless declared as such. Consider:

from collections.abc import Callable
from typing import Any, Concatenate

class MyClass:
    def method(self, **kwargs: Any) -> None:
        return


def check[**P](func: Callable[Concatenate[Any, P], None], *args: P.args, **kwargs: P.kwargs) -> None:
    func(MyClass(), *args, **kwargs)

check(MyClass.method, self=1)  # E: Argument 1 to "check" has incompatible type "Callable[[Arg(MyClass, 'self'), KwArg(Any)], None]"; expected "Callable[[Any, KwArg(Any)], None]"  [arg-type]
# Runtime: TypeError: MyClass.method() got multiple values for argument 'self'

playground

self is never positional-only unless declared as such.

In that case, why doesn't my first example (https://mypy-play.net/?mypy=master&python=3.12&flags=strict&gist=5d5a1b27f2838371bee58b2d9c9a7721) produce an error?

Because there's no fallback **kwargs or explicit self kw-only argument - your Concatenate strips the first argument, and you're left with one, positional-or-keyword argument x, there's no uncertainty whether self can be also passed as kwarg later.

Concatenate treats that as posonly, and def method(self, /, **kwargs) won't raise the runtime error, so we shouldn't reject it inside check.

Ok, that makes sense now, thanks! I found a solution by replacing the Callable with a Protocol that includes the self parameter.