Automatically use `Self` type even if it doesn't appear in method annotation

This is a follow up for https://github.com/python/mypy/pull/14041

This example gives an error:

from typing import Self

class C:
    x: Self
    def meth(self) -> None:
        self.x = self  # E: Incompatible types in assignment (expression has type "C", variable has type "Self")

Although it is unfortunate, technically this is required by PEP 484, that says that if no annotation is given, self has a type of current class (note also we can't bind self type for self.x expression giving it type C, as this will open another unsafety). This can be avoided by using e.g. self: Self (or generally Self type anywhere in the signature).

It looks like there can be only two solutions:

• Always infer Self type for self. This will cause a big performance penalty and may be surprising for users who are not familiar with Self (if they use reveal_type(self)).
• Use some heuristic and only infer Self where otherwise we will have this problem. For example, infer Self if an attribute with type containing Self is used anywhere in a method.

I am leaning towards the latter, but didn't want to do this until we get some more experience.

Start by reading the follow-up context in PR #14041 and reproducing the example with Self and self.x = self. Review the relevant PEP 484 behavior and compare the two proposed inference approaches. Done means agreeing on an approach and making the example type-check without introducing the stated unsafety or broad unintended behavior.