### 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)

switch (GLOBAL_GET("editor/naming/node_name_casing").operator int()) {
		case NAME_CASING_PASCAL_CASE:
			return p_name.to_pascal_case();
		case NAME_CASING_CAMEL_CASE:
			return p_name.to_camel_case();
		case NAME_CASING_SNAKE_CASE:
			return p_name.to_snake_case();
	}
	return p_name;
}
void Node::_validate_child_name(Node *p_child, bool p_force_human_readable) {
	
	if (p_force_human_readable) {
		
		StringName name = p_child->data.name;
		_generate_serial_child_name(p_child, name);
		p_child->data.name = name;
	} else {
		
		
		bool unique = true;
		if (p_child->data.name == StringName()) {
			
			unique = false;
		} else {
			const Node *const *existing = data.children.getptr(p_child->data.name);
			unique = !existing || *existing == p_child;