Signatures of *in-place binary operation* and *binary operation* are incompatible

Bug Report

If I define custom binary operations (both regular & in-place versions) using __dunder__ methods like __add__ & __iadd__, I'm having odd

Signatures of "__iadd__" and "__add__" are incompatible

and I don't understand why, what is a "compatibility" the error is telling about?

To Reproduce

from __future__ import annotations

from typing import Any, overload


class MyClass:
    @overload
    def __add__(self, other: MyClass) -> MyClass:
        ...

    @overload
    def __add__(self, other: Any) -> Any:
        ...

    def __add__(self, other: Any) -> Any:
        return (self
                if isinstance(other, MyClass)
                else NotImplemented)

    @overload
    def __iadd__(self, other: MyClass) -> MyClass:
        ...

    @overload
    def __iadd__(self, other: Any) -> Any:
        ...

    def __iadd__(self, other: Any) -> Any:
        if not isinstance(other, MyClass):
            return NotImplemented
        return self

https://mypy-play.net/?mypy=latest&python=3.8&gist=819e2627d0a17df446a5d7b2b3631f11

Expected Behavior

Ideally as a user of static type analyzer I want to get an error when I misuse a type hint for parameters/return type and get details about what's wrong with my code according to some rules, current message is too vague and the error isn't going away even when I put typing.Any everywhere in one of the methods annotations (only when I remove all typing.overloads). This is also the case when I use typing.Self instead of MyClass

Actual Behavior

error: Signatures of "__iadd__" and "__add__" are incompatible  [misc]

Your Environment

• Mypy version used: mypy 1.1.1 (compiled: yes)
• Mypy command-line flags: both none & --strict
• Mypy configuration options from mypy.ini (and other config files): none
• Python version used: Python3.8

Start with the linked mypy-play reproduction and compare how the checker evaluates the overloaded add and iadd methods. Trace the compatibility check for these binary-operation dunder signatures and establish the intended diagnostic or accepted typing behavior. Done means the reported case has a clear, justified result and a regression test covers it.