(🐞) call-overload error when calling overloaded constructors which involve exhaustive Literal cases (e.g. for bool type argument)

Bug Report

Mypy raises call-overload when attempting to call an overloaded superclass constructor, if the overload hinges on literal True and False values and the call passes a bool value.

This is related to issue https://github.com/python/mypy/issues/8330

To Reproduce

class A:

    x: bool

    @overload
    def __init__(self, x: Literal[True]) -> None:
        ...
    @overload
    def __init__(self, x: Literal[False] = False) -> None:
        ...

    def __init__(self, x: bool = False) -> None:
        super().__init__()
        self.x = x

class B(A):

    @overload
    def __init__(self, x: Literal[True]) -> None:
        ...
    @overload
    def __init__(self, x: Literal[False] = False) -> None:
        ...

    def __init__(self, x: bool = False) -> None:
        super().__init__(x) # Mypy error: call-overload

# No overload variant of "__init__" of "A" matches argument type "bool"
# Possible overload variants:
#     def __init__(self, x: Literal[True]) -> None
#     def __init__(self, x: Literal[False] = ...) -> NoneMypy

class C(A):

    @overload
    def __init__(self, x: Literal[True]) -> None:
        ...
    @overload
    def __init__(self, x: Literal[False] = False) -> None:
        ...

    def __init__(self, x: bool = False) -> None:
        if x:
            super().__init__(x)  # OK
        else:
            super().__init__(x)  # OK

Please note: this is intended as a minimal example, not as an interesting example. I am happyt to produce interesting examples if they provide additional motivation to tackle this issue.

Expected Behavior

Because the bool type is fully covered by the Literal[True] and Literal[False] cases, it should be possible for Mypy to infer that the call super().__init__(x) is correct in the B constructor.

Actual Behavior

No overload variant of "__init__" of "A" matches argument type "bool"
Possible overload variants:
    def __init__(self, x: Literal[True]) -> None
    def __init__(self, x: Literal[False] = ...) -> NoneMypy

Your Environment

• Mypy version used: mypy 1.7.1 (compiled: yes)
• Mypy command-line flags: --strict
• Python version used: 3.12.0 64-bit

Start by reproducing the minimal example with mypy 1.7.1 and --strict, focusing on the super().init(x) call in class B and comparing it with class C. Trace the overload checking involved in exhaustive Literal[True] and Literal[False] cases; done means the B constructor no longer produces call-overload and the regression is covered by a test.