### 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)

ADD_PROPERTY(PropertyInfo(Variant::INT, "process_thread_group", PROPERTY_HINT_ENUM, "Inherit,Main Thread,Sub Thread"), "set_process_thread_group", "get_process_thread_group");
	ADD_PROPERTY(PropertyInfo(Variant::INT, "process_thread_group_order"), "set_process_thread_group_order", "get_process_thread_group_order");
	ADD_PROPERTY(PropertyInfo(Variant::INT, "process_thread_messages", PROPERTY_HINT_FLAGS, "Process,Physics Process"), "set_process_thread_messages", "get_process_thread_messages");
	ADD_GROUP("Editor Description", "editor_");
	ADD_PROPERTY(PropertyInfo(Variant::STRING, "editor_description", PROPERTY_HINT_MULTILINE_TEXT), "set_editor_description", "get_editor_description");
	GDVIRTUAL_BIND(_process, "delta");
	GDVIRTUAL_BIND(_physics_process, "delta");
	GDVIRTUAL_BIND(_enter_tree);
	GDVIRTUAL_BIND(_exit_tree);
	GDVIRTUAL_BIND(_ready);
	GDVIRTUAL_BIND(_get_configuration_warnings);
	GDVIRTUAL_BIND(_input, "event");
	GDVIRTUAL_BIND(_shortcut_input, "event");
	GDVIRTUAL_BIND(_unhandled_input, "event");
	GDVIRTUAL_BIND(_unhandled_key_input, "event");
}
String Node::_get_name_num_separator() {
	switch (GLOBAL_GET("editor/naming/node_name_num_separator").operator int()) {
		case 0:
			return "";
		case 1:
			return " ";
		case 2:
			return "_";
		case 3:
			return "-";
	}
	return " ";
}
Node::Node() {