Cleanup a lot of the bootup state management.

Core/Debugger/WebSocket.cpp

@@ -99,10 +99,6 @@ static void UpdateConnected(int delta) {
 }
 
 static void WebSocketNotifyLifecycle(CoreLifecycle stage) {
-	// We'll likely already be locked during the reboot.
-	if (PSP_IsRebooting())
-		return;
-
 	switch (stage) {
 	case CoreLifecycle::STARTING:
 	case CoreLifecycle::STOPPING: