### Godot version

v4.2.dev.custom_build [0ca854232]

### System information

Pop Os 22.04 lts 12th Gen Intel® Core™ i7-12700H × 20 NVIDIA RTX A2000 8GB 32.0GB  ram

### Issue description

A node that has a script attached to it and it has a couple of child nodes (type of a child node doesn't matter). In the script you have an export variable of type Node. You save the scene into a file and you add it in level scene. When you start to duplicate that scene in the level and you'll hover over exported variable to show a node path, it will show an incorrect path. 


https://github.com/godotengine/godot/assets/33091666/75088d1b-c014-41e0-bae3-46610eccbad1



### Steps to reproduce

1. create a scene with a node and a child node.
2. attach a script to the parent node and create an export variable of type Node
3. assign child node to that exported variable through the editor
4. save the scene and create a level scene where you are going to add just saved scene.
5. _Possibly requires a reboot of the engine before seeing the bug_
6. start duplicating nodes in the level scene

### Minimal reproduction project

[NodeTest.zip](https://github.com/godotengine/godot/files/12781547/NodeTest.zip)

GDVIRTUAL_CALL(_ready);
		} break;
		case NOTIFICATION_POSTINITIALIZE: {
			data.in_constructor = false;
		} break;
		case NOTIFICATION_PREDELETE: {
			if (data.inside_tree && !Thread::is_main_thread()) {
				cancel_free();
				ERR_PRINT("Attempted to free a node that is currently added to the SceneTree from a thread. This is not permitted, use queue_free() instead. Node has not been freed.");
				return;
			}
			if (data.owner) {
				_clean_up_owner();
			}
			while (!data.owned.is_empty()) {
				Node *n = data.owned.back()->get();
				n->_clean_up_owner(); 
			}
			if (data.parent) {
				data.parent->remove_child(this);
			}
			
			while (data.children.size()) {
				Node *child = data.children.last()->value; 
				memdelete(child);
			}
		} break;
	}
}
void Node::_propagate_ready() {