### 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)

Error copy_from(const Ref<SceneState> &p_scene_state);
	bool can_instantiate() const;
	Node *instantiate(GenEditState p_edit_state) const;
	Ref<SceneState> get_base_scene_state() const;
	void update_instance_resource(String p_path, Ref<PackedScene> p_packed_scene);
	
	int get_node_count() const;
	StringName get_node_type(int p_idx) const;
	StringName get_node_name(int p_idx) const;
	NodePath get_node_path(int p_idx, bool p_for_parent = false) const;
	NodePath get_node_owner_path(int p_idx) const;
	Ref<PackedScene> get_node_instance(int p_idx) const;
	String get_node_instance_placeholder(int p_idx) const;
	bool is_node_instance_placeholder(int p_idx) const;
	Vector<StringName> get_node_groups(int p_idx) const;
	int get_node_index(int p_idx) const;
	int get_node_property_count(int p_idx) const;
	StringName get_node_property_name(int p_idx, int p_prop) const;
	Variant get_node_property_value(int p_idx, int p_prop) const;
	Vector<String> get_node_deferred_nodepath_properties(int p_idx) const;
	int get_connection_count() const;
	NodePath get_connection_source(int p_idx) const;
	StringName get_connection_signal(int p_idx) const;
	NodePath get_connection_target(int p_idx) const;
	StringName get_connection_method(int p_idx) const;
	int get_connection_flags(int p_idx) const;
	int get_connection_unbinds(int p_idx) const;
	Array get_connection_binds(int p_idx) const;
	bool has_connection(const NodePath &p_node_from, const StringName &p_signal, const NodePath &p_node_to, const StringName &p_method, bool p_no_inheritance = false);
	Vector<NodePath> get_editable_instances() const;