ヘルスチェックの設定を公式ドキュメントを参考に追加、クラスタデフォルトのヘルスチェックの設定を追加

https://doc.akka.io/libraries/akka-management/current/healthchecks.html#configuring-health-checks

sample/src/main/resources/application.conf

@@ -53,6 +53,13 @@ akka {
         discovery-method = kubernetes-api
       }
     }
+    health-checks {
+      readiness-checks {
+        # Default health check for cluster. Overwrite the setting to replace it with
+        # your implementation or set it to "" (empty string) to disable this check.
+        cluster-membership = "akka.management.cluster.scaladsl.ClusterMembershipCheck"
+      }
+    }
   }
 
   coordinated-shutdown.exit-jvm = on