### 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)

FLAG_ID_IS_PATH = (1 << 30),
		TYPE_INSTANTIATED = 0x7FFFFFFF,
		FLAG_INSTANCE_IS_PLACEHOLDER = (1 << 30),
		FLAG_PATH_PROPERTY_IS_NODE = (1 << 30),
		FLAG_PROP_NAME_MASK = FLAG_PATH_PROPERTY_IS_NODE - 1,
		FLAG_MASK = (1 << 24) - 1,
	};
	enum GenEditState {
		GEN_EDIT_STATE_DISABLED,
		GEN_EDIT_STATE_INSTANCE,
		GEN_EDIT_STATE_MAIN,
		GEN_EDIT_STATE_MAIN_INHERITED,
	};
	struct PackState {
		Ref<SceneState> state;
		int node = -1;
	};
	static void set_disable_placeholders(bool p_disable);
	int find_node_by_path(const NodePath &p_node) const;
	Variant get_property_value(int p_node, const StringName &p_property, bool &found) const;
	bool is_node_in_group(int p_node, const StringName &p_group) const;
	bool is_connection(int p_node, const StringName &p_signal, int p_to_node, const StringName &p_to_method) const;
	void set_bundled_scene(const Dictionary &p_dictionary);
	Dictionary get_bundled_scene() const;
	Error pack(Node *p_scene);
	void set_path(const String &p_path);
	String get_path() const;
	void clear();