### 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)

GDCLASS(EditorPropertyNodePath, EditorProperty);
	Button *assign = nullptr;
	Button *clear = nullptr;
	SceneTreeDialog *scene_tree = nullptr;
	NodePath base_hint;
	bool use_path_from_scene_root = false;
	bool pointer_mode = false;
	Vector<StringName> valid_types;
	void _node_selected(const NodePath &p_path);
	void _node_assign();
	void _node_clear();
	bool can_drop_data_fw(const Point2 &p_point, const Variant &p_data, Control *p_from) const;
	void drop_data_fw(const Point2 &p_point, const Variant &p_data, Control *p_from);
	bool is_drop_valid(const Dictionary &p_drag_data) const;
	String _get_meta_pointer_property() const;
	virtual Variant _get_cache_value(const StringName &p_prop, bool &r_valid) const override;
	virtual StringName _get_revert_property() const override;
protected:
	virtual void _set_read_only(bool p_read_only) override;
	static void _bind_methods();
	void _notification(int p_what);
public:
	virtual void update_property() override;
	void setup(const NodePath &p_base_hint, Vector<StringName> p_valid_types, bool p_use_path_from_scene_root = true, bool p_pointer_mode = false);
	EditorPropertyNodePath();
};
class EditorPropertyRID : public EditorProperty {