Add hint for AsyncIterator incompatible return type (#15883)

For issue described in #5070 and documented in #14973, add a contextual
link to the docs.

mypy/messages.py

@@ -1310,6 +1310,22 @@ def return_type_incompatible_with_supertype(
             code=codes.OVERRIDE,
         )
 
+        original = get_proper_type(original)
+        override = get_proper_type(override)
+        if (
+            isinstance(original, Instance)
+            and isinstance(override, Instance)
+            and override.type.fullname == "typing.AsyncIterator"
+            and original.type.fullname == "typing.Coroutine"
+            and len(original.args) == 3
+            and original.args[2] == override
+        ):
+            self.note(f'Consider declaring "{name}" in {target} without "async"', context)
+            self.note(
+                "See https://mypy.readthedocs.io/en/stable/more_types.html#asynchronous-iterators",
+                context,
+            )
+
     def override_target(self, name: str, name_in_super: str, supertype: str) -> str:
         target = f'supertype "{supertype}"'
         if name_in_super != name:

test-data/unit/check-async-await.test

@@ -1021,3 +1021,19 @@ def coro() -> Generator[int, None, None]:
 reveal_type(coro)  # N: Revealed type is "def () -> typing.AwaitableGenerator[builtins.int, None, None, typing.Generator[builtins.int, None, None]]"
 [builtins fixtures/async_await.pyi]
 [typing fixtures/typing-async.pyi]
+
+[case asyncIteratorInProtocol]
+from typing import AsyncIterator, Protocol
+
+class P(Protocol):
+    async def launch(self) -> AsyncIterator[int]:
+        raise BaseException
+
+class Launcher(P):
+    def launch(self) -> AsyncIterator[int]:  # E: Return type "AsyncIterator[int]" of "launch" incompatible with return type "Coroutine[Any, Any, AsyncIterator[int]]" in supertype "P" \
+                                             # N: Consider declaring "launch" in supertype "P" without "async" \
+                                             # N: See https://mypy.readthedocs.io/en/stable/more_types.html#asynchronous-iterators
+        raise BaseException
+
+[builtins fixtures/async_await.pyi]
+[typing fixtures/typing-async.pyi]