website: Remove next task button and load new task immediately

Also disable the task inputs while the task is submitted and before the new task is ready in case the users network is slow or something.

website/src/hooks/tasks/useGenericTaskAPI.tsx

@@ -24,6 +24,7 @@ export const useGenericTaskAPI = <TaskType extends BaseTask>(taskApiEndpoint: st
     onSuccess: async (response) => {
       const newTask: ConcreteTaskResponse = await response.json();
       setTasks((oldTasks) => [...oldTasks, newTask]);
+      mutate();
     },
   });