🐛 Fix healthcheck in api-server (#6662)

services/api-server/src/simcore_service_api_server/core/health_checker.py

@@ -69,7 +69,9 @@ async def teardown(self):
 
     @property
     def healthy(self) -> bool:
-        return self._health_check_failure_count <= self._allowed_health_check_failures
+        return self._rabbit_client.healthy and (
+            self._health_check_failure_count <= self._allowed_health_check_failures
+        )  # https://github.com/ITISFoundation/osparc-simcore/pull/6662
 
     @property
     def health_check_failure_count(self) -> NonNegativeInt:
@@ -82,9 +84,6 @@ async def _background_task_method(self):
         while self._dummy_queue.qsize() > 0:
             _ = self._dummy_queue.get_nowait()
         try:
-            if not self._rabbit_client.healthy:
-                self._increment_health_check_failure_count()
-                return
             await asyncio.wait_for(
                 self._rabbit_client.publish(
                     self._dummy_message.channel_name, self._dummy_message