### 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)

name_string = name_string.substr(0, name_last_index + nnsep.length());
	} else {
		nums = "";
	}
	for (;;) {
		StringName attempt = name_string + nums;
		existing = data.children.getptr(attempt);
		bool exists = existing != nullptr && *existing != p_child;
		if (!exists) {
			name = attempt;
			return;
		} else {
			if (nums.length() == 0) {
				
				nums = "2";
				name_string += nnsep; 
			} else {
				nums = increase_numeric_string(nums);
			}
		}
	}
}
Node::InternalMode Node::get_internal_mode() const {
	return data.internal_mode;
}
void Node::_add_child_nocheck(Node *p_child, const StringName &p_name, InternalMode p_internal_mode) {
	
	p_child->data.name = p_name;
	data.children.insert(p_name, p_child);
	p_child->data.internal_mode = p_internal_mode;