[scheduler]: Fix a bug with non-nestable tasks.

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 1e6b25ea4f4d3d59c10eace066c63957cc3411e1..9e3e3d9097cb5f43e2a0760feceba12e956b98dc 100644
--- a/components/scheduler/child/task_queue_manager.cc
+++ b/components/scheduler/child/task_queue_manager.cc
@@ -283,6 +283,9 @@ bool TaskQueueManager::ProcessTaskFromWorkQueue(
     // arbitrarily delayed so the additional delay should not be a problem.
     main_task_runner_->PostNonNestableTask(pending_task.posted_from,
                                            pending_task.task);
+    // Even although we haven't actually run this task yet, we do set it as
+    // the out_previous_task below because it might be our only chance to
+    // wake up an after-wakeup queue.
   } else {
     TRACE_TASK_EXECUTION("TaskQueueManager::ProcessTaskFromWorkQueue",
                          pending_task);
@@ -301,10 +304,10 @@ bool TaskQueueManager::ProcessTaskFromWorkQueue(
       FOR_EACH_OBSERVER(base::MessageLoop::TaskObserver, task_observers_,
                         DidProcessTask(pending_task));
     }
-
-    pending_task.task.Reset();
-    *out_previous_task = pending_task;
   }
+
+  pending_task.task.Reset();
+  *out_previous_task = pending_task;
   return false;
 }