Address comment: Use signal actor for async background task test

Closes: #49451
Signed-off-by: Chi-Sheng Liu <[email protected]>

python/ray/tests/test_actor_failures.py

@@ -1044,6 +1044,8 @@ def test_exit_actor_async_actor_nested_task(shutdown_only, tmp_path):
     assert not temp_file_atexit.exists()
     assert not temp_file_after_exit_actor.exists()
 
+    signal = SignalActor.remote()
+
     @ray.remote
     class AsyncActor:
         def __init__(self):
@@ -1052,24 +1054,19 @@ def f():
 
             atexit.register(f)
 
-        async def start_exit_task(self):
-            asyncio.create_task(self.exit())
+        async def start_exit_task(self, signal):
+            asyncio.create_task(self.exit(signal))
 
-        async def exit(self):
+        async def exit(self, signal):
+            await signal.wait.remote()
             exit_actor()
             # The following code should not be executed.
             temp_file_after_exit_actor.touch()
 
     a = AsyncActor.remote()
     ray.get(a.__ray_ready__.remote())
-    with pytest.raises(ray.exceptions.RayActorError) as exc_info:
-        ray.get(a.start_exit_task.remote())
-    assert (
-        # Exited when task execution returns
-        "exit_actor()" in str(exc_info.value)
-        # Exited during periodical check in worker
-        or "User requested to exit the actor" in str(exc_info.value)
-    )
+    ray.get(a.start_exit_task.remote(signal))
+    ray.get(signal.send.remote())
 
     def verify():
         return temp_file_atexit.exists()