[border-agent] fix meshcop service update issue (#11320)

This commit fixes an issue in BorderAgent when handling Notifier
events.

If the events contain 'Epskc' and BA is not running, then the meshcop
service update will be skipped.

src/core/meshcop/border_agent.cpp

@@ -172,6 +172,12 @@ void BorderAgent::HandleNotifierEvents(Events aEvents)
         }
     }
 
+    if (aEvents.ContainsAny(kEventThreadRoleChanged | kEventThreadExtPanIdChanged | kEventThreadNetworkNameChanged |
+                            kEventThreadBackboneRouterStateChanged | kEventActiveDatasetChanged))
+    {
+        PostNotifyMeshCoPServiceChangedTask();
+    }
+
     if (aEvents.ContainsAny(kEventPskcChanged))
     {
         Pskc pskc;
@@ -186,12 +192,6 @@ void BorderAgent::HandleNotifierEvents(Events aEvents)
         pskc.Clear();
     }
 
-    if (aEvents.ContainsAny(kEventThreadRoleChanged | kEventThreadExtPanIdChanged | kEventThreadNetworkNameChanged |
-                            kEventThreadBackboneRouterStateChanged | kEventActiveDatasetChanged))
-    {
-        PostNotifyMeshCoPServiceChangedTask();
-    }
-
 exit:
     return;
 }