### 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)

void Node::_update_children_cache_impl() const {
	
	data.children_cache.resize(data.children.size());
	int idx = 0;
	for (const KeyValue<StringName, Node *> &K : data.children) {
		data.children_cache[idx] = K.value;
		idx++;
	}
	
	data.children_cache.sort_custom<ComparatorByIndex>();
	
	data.external_children_count_cache = 0;
	data.internal_children_back_count_cache = 0;
	data.internal_children_front_count_cache = 0;
	for (uint32_t i = 0; i < data.children_cache.size(); i++) {
		switch (data.children_cache[i]->data.internal_mode) {
			case INTERNAL_MODE_DISABLED: {
				data.children_cache[i]->data.index = data.external_children_count_cache++;
			} break;
			case INTERNAL_MODE_FRONT: {
				data.children_cache[i]->data.index = data.internal_children_front_count_cache++;
			} break;
			case INTERNAL_MODE_BACK: {
				data.children_cache[i]->data.index = data.internal_children_back_count_cache++;
			} break;
		}
	}
	data.children_cache_dirty = false;
}
int Node::get_child_count(bool p_include_internal) const {