### 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)

if (!data.viewport && data.parent) {
		data.viewport = data.parent->data.viewport;
	}
	data.inside_tree = true;
	for (KeyValue<StringName, GroupData> &E : data.grouped) {
		E.value.group = data.tree->add_to_group(E.key, this);
	}
	notification(NOTIFICATION_ENTER_TREE);
	GDVIRTUAL_CALL(_enter_tree);
	emit_signal(SceneStringNames::get_singleton()->tree_entered);
	data.tree->node_added(this);
	if (data.parent) {
		Variant c = this;
		const Variant *cptr = &c;
		data.parent->emit_signalp(SNAME("child_entered_tree"), &cptr, 1);
	}
	data.blocked++;
	
	for (KeyValue<StringName, Node *> &K : data.children) {
		if (!K.value->is_inside_tree()) { 
			K.value->_propagate_enter_tree();
		}
	}
	data.blocked--;
#ifdef DEBUG_ENABLED
	SceneDebugger::add_to_cache(data.scene_file_path, this);
#endif
	
}
void Node::_propagate_after_exit_tree() {