Reland: Explicitly track the scheduler task enqueueing order in a new field

components/scheduler/child/task_queue_manager.cc

Index: components/scheduler/child/task_queue_manager.cc
diff --git a/components/scheduler/child/task_queue_manager.cc b/components/scheduler/child/task_queue_manager.cc
index c557665ab7a4b6a5fac49b02fa6f58a461135f56..f080a96f462629e9354aea5da13e108f53121efc 100644
--- a/components/scheduler/child/task_queue_manager.cc
+++ b/components/scheduler/child/task_queue_manager.cc
@@ -125,11 +125,6 @@ void TaskQueueManager::UpdateWorkQueues(
     // as the iterator isn't the element being delated.
     if (queue->work_queue().empty())
         queue->UpdateWorkQueue(&lazy_now, should_trigger_wakeup, previous_task);
-    if (!queue->work_queue().empty()) {
-      // Currently we should not be getting tasks with delayed run times in any
-      // of the work queues.
-      DCHECK(queue->work_queue().front().delayed_run_time.is_null());
-    }
   }
 }
 
@@ -201,7 +196,8 @@ bool TaskQueueManager::ProcessTaskFromWorkQueue(
     base::PendingTask* out_previous_task) {
   DCHECK(main_thread_checker_.CalledOnValidThread());
   scoped_refptr<DeletionSentinel> protect(deletion_sentinel_);
-  base::PendingTask pending_task = queue->TakeTaskFromWorkQueue();
+  // TODO(alexclarke): consider std::move() when allowed.
+  internal::TaskQueueImpl::Task pending_task = queue->TakeTaskFromWorkQueue();
 
   if (queue->GetQuiescenceMonitored())
     task_was_run_on_quiescence_monitored_queue_ = true;