Change WokerThread to use a blink::WebThread

Source/core/inspector/WorkerDebuggerAgent.cpp

Index: Source/core/inspector/WorkerDebuggerAgent.cpp
diff --git a/Source/core/inspector/WorkerDebuggerAgent.cpp b/Source/core/inspector/WorkerDebuggerAgent.cpp
index c5fede741f4eb0ee8263aae9578346fd80d3957b..88f4b9c2166b8f1937bd1be610b1351b6109dc95 100644
--- a/Source/core/inspector/WorkerDebuggerAgent.cpp
+++ b/Source/core/inspector/WorkerDebuggerAgent.cpp
@@ -50,7 +50,9 @@ public:
     {
         // Process all queued debugger commands. WorkerThread is certainly
         // alive if this task is being executed.
-        while (MessageQueueMessageReceived == m_thread->runDebuggerTask(WorkerRunLoop::DontWaitForMessage)) { }
+        m_thread->willEnterNestedLoop();
+        while (MessageQueueMessageReceived == m_thread->runDebuggerTask(WorkerThread::DontWaitForMessage)) { }
+        m_thread->didLeaveNestedLoop();
     }
 
 private: