### Godot version

v4.0.alpha11.official [afdae67cc] (when the feature was added) and newer (still happens in RC6)

### System information

Windows 10

### Issue description

I'm unable to handle when the user sets an exported node property (this feature: https://github.com/godotengine/godot/pull/62185) from a setter in the editor (tool script).

I don't know if this is intentional or not, but for me it was unexpected. I had to revert back to `NodePath`s.

### Steps to reproduce

- Create a scene
- Attach a script to a node
- Add `@tool` at the top of the script
- Export a node property with a setter, preferably with an easy way to see if it executed:
	```
	@export var node:Node:
		set (mod_value):
			prints("node", mod_value)
			node = mod_value
	```
- Save, close and open again the scene to make sure the tool script is running in the editor
- Set the node property from the inspector
- Observe that the setter didn't run

The setter is not bypassed when running the game, it is only bypassed in the editor.

We can compare with a `NodePath` property, which setter is not bypassed regardless if it is in the editor or in game runtime.

### Minimal reproduction project

[nodepath.zip](https://github.com/godotengine/godot/files/10840411/nodepath.zip)

#ifndef PACKED_SCENE_H
#define PACKED_SCENE_H
#include "core/io/resource.h"
#include "scene/main/node.h"
class SceneState : public RefCounted {
	GDCLASS(SceneState, RefCounted);
	Vector<StringName> names;
	Vector<Variant> variants;
	Vector<NodePath> node_paths;
	Vector<NodePath> editable_instances;
	mutable HashMap<NodePath, int> node_path_cache;
	mutable HashMap<int, int> base_scene_node_remap;
	int base_scene_idx = -1;
	enum {
		NO_PARENT_SAVED = 0x7FFFFFFF,
		NAME_INDEX_BITS = 18,
		NAME_MASK = (1 << NAME_INDEX_BITS) - 1,
	};
	struct NodeData {
		int parent = 0;
		int owner = 0;
		int type = 0;
		int name = 0;
		int instance = 0;
		int index = 0;
		struct Property {
			int name = 0;
			int value = 0;
		};