### 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)

int add_name(const StringName &p_name);
	int add_value(const Variant &p_value);
	int add_node_path(const NodePath &p_path);
	int add_node(int p_parent, int p_owner, int p_type, int p_name, int p_instance, int p_index);
	void add_node_property(int p_node, int p_name, int p_value, bool p_deferred_node_path = false);
	void add_node_group(int p_node, int p_group);
	void set_base_scene(int p_idx);
	void add_connection(int p_from, int p_to, int p_signal, int p_method, int p_flags, int p_unbinds, const Vector<int> &p_binds);
	void add_editable_instance(const NodePath &p_path);
	virtual void set_last_modified_time(uint64_t p_time) { last_modified_time = p_time; }
	uint64_t get_last_modified_time() const { return last_modified_time; }
	
	static String get_meta_pointer_property(const String &p_property);
	SceneState();
};
VARIANT_ENUM_CAST(SceneState::GenEditState)
class PackedScene : public Resource {
	GDCLASS(PackedScene, Resource);
	RES_BASE_EXTENSION("scn");
	Ref<SceneState> state;
	void _set_bundled_scene(const Dictionary &p_scene);
	Dictionary _get_bundled_scene() const;
protected:
	virtual bool editor_can_reload_from_file() override { return false; } 
	static void _bind_methods();
	virtual void reset_state() override;
public:
	static const String META_POINTER_PROPERTY_BASE;
	enum GenEditState {