update

Added an experimental "NetworkObjectBridge" icon (programmer art alert).
Added some additional script to handle moving the GhostAdapter and NetworkObject bridge to the top of the GameObject's components where GhostAdapter is first and then NetworkObjectBridge is 2nd.

Removed silly code to get the root transform.

Author: NoelStephensUnity

com.unity.netcode.gameobjects/Editor/Icons.meta

@@ -321,20 +321,6 @@ private void OnEnable()
             CheckForNetworkObject((target as NetworkBehaviour).gameObject);
         }
 
-        /// <summary>
-        /// Recursively finds the root parent of a <see cref="Transform"/>
-        /// </summary>
-        /// <param name="transform">The current <see cref="Transform"/> we are inspecting for a parent</param>
-        /// <returns>the root parent for the first <see cref="Transform"/> passed into the method</returns>
-        public static Transform GetRootParentTransform(Transform transform)
-        {
-            if (transform.parent == null || transform.parent == transform)
-            {
-                return transform;
-            }
-            return GetRootParentTransform(transform.parent);
-        }
-
         /// <summary>
         /// Used to determine if a GameObject has one or more NetworkBehaviours but
         /// does not already have a NetworkObject component.  If not it will notify
@@ -358,7 +344,7 @@ public static void CheckForNetworkObject(GameObject gameObject, bool networkObje
             }
 
             // Now get the root parent transform to the current GameObject (or itself)
-            var rootTransform = GetRootParentTransform(gameObject.transform);
+            var rootTransform = gameObject.transform.root;
             if (!rootTransform.TryGetComponent<NetworkManager>(out var networkManager))
             {
                 networkManager = rootTransform.GetComponentInChildren<NetworkManager>();

com.unity.netcode.gameobjects/Editor/Icons/NOBridgeIcon.png

@@ -355,6 +355,8 @@ private void CheckForInScenePlaced()
         [SerializeField]
         internal bool HasGhost;
 
+        [HideInInspector]
+        [SerializeField]
         internal bool HadBridge;
 
         private void UnifiedValidation()
@@ -364,13 +366,31 @@ private void UnifiedValidation()
             HasGhost = GhostAdapter != null;
             if (HasGhost && NetworkObjectBridge == null)
             {
-                if (!HadBridge)
                 {
                     NetworkObjectBridge = gameObject.AddComponent<NetworkObjectBridge>();
                     HadBridge = true;
                     // Transform synchronization is handled by unified netcode
                     SynchronizeTransform = false;
                 }
+
+                // Move the bridge to the top
+                while (UnityEditorInternal.ComponentUtility.MoveComponentUp(NetworkObjectBridge))
+                {
+                    // Keep moving until it can't go higher
+                }
+
+                // Now move the GhostAdapter to the top so it is above NetworkObjectBridge
+                while (UnityEditorInternal.ComponentUtility.MoveComponentUp(GhostAdapter))
+                {
+                    // Keep moving until it can't go higher
+                }
+                
+                EditorUtility.SetDirty(gameObject);
+            }
+            else if (HadBridge && !HasGhost && !NetworkObjectBridge)
+            {
+                HadBridge = false;
+                SynchronizeTransform = true;
             }
         }
 #endif