Confusing error message for property with @overloaded function

The following does not seem to work:

from typing import overload


class Example:

	@overload
	def fun(self, p: int) -> int: ...
	@overload
	def fun(self, p: str) -> str: ...

	def fun(self, p=1):
		if isinstance(p, int):
			return 'foo'
		else:
			return 'bar'

	prop = property(fun)

Argument 1 to "property" has incompatible type overloaded function; expected "Optional[Callable[[Any], Any]]"

Is this a bug or expected?
Also, fun(0) returns a string instead of an int as specified in the stub, but mypy doesn't seem to catch this. Again, bug or expected?

Start by reproducing the provided Python example and tracing the diagnostics for passing an overloaded method to property and for checking its implementation return type. Done means the expected behavior is established and the resulting diagnostics or checking behavior are covered by a regression test.