Could you also add a concrete class (e.g., COverload) that has a suitable overloaded method, and test that issubclass can be used to narrow down from Type[Union[COverload, E]], similar to above around line 2218?

So while trying the add the test you proposed I seem to have stumbled across another bug.

The if block successfully narrows down the Union to Type[COverload] but the else block
on the other hand fails to do the same with E, revealing the type as the original Union.

Would you happen to know where in mypy the type inference of if / else statements is handled?
I imagine that change similar to non_method_protocol_members() will have to be made there,
but I'm not quite sure where to look.

Examples

class COverload:
    x: str
    @overload
    def meth(self, a: int) -> float: ...
    @overload
    def meth(self, a: str) -> Sequence[float]: ...
    def meth(self, a):
        pass

cls_overload: Type[Union[COverload, E]]
if issubclass(cls_overload, POverload):
    reveal_type(cls_overload)  # N: Revealed type is 'Type[__main__.COverload]'
else:
    reveal_type(cls_overload)  # N: Revealed type is 'Type[__main__.E]'

The test output:

Expected:
  ...
  main:45: note: Revealed type is 'Type[__main__.COverload]'
  main:47: note: Revealed type is 'Type[__main__.E]' (diff)
Actual:
  ...
  main:45: note: Revealed type is 'Type[__main__.COverload]'
  main:47: note: Revealed type is 'Union[Type[__main__.COverload], Type[__main__.E]]' (diff)

Could you please open a new issue about it?

Could you please open a new issue about it?

I just created an issue at #12228.