### 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(EditorPropertyTextEnum, EditorProperty);
	HBoxContainer *default_layout = nullptr;
	HBoxContainer *edit_custom_layout = nullptr;
	OptionButton *option_button = nullptr;
	Button *edit_button = nullptr;
	LineEdit *custom_value_edit = nullptr;
	Button *accept_button = nullptr;
	Button *cancel_button = nullptr;
	Vector<String> options;
	bool string_name = false;
	bool loose_mode = false;
	void _emit_changed_value(String p_string);
	void _option_selected(int p_which);
	void _edit_custom_value();
	void _custom_value_submitted(String p_value);
	void _custom_value_accepted();
	void _custom_value_canceled();
protected:
	virtual void _set_read_only(bool p_read_only) override;
	static void _bind_methods();
	void _notification(int p_what);
public:
	void setup(const Vector<String> &p_options, bool p_string_name = false, bool p_loose_mode = false);
	virtual void update_property() override;
	EditorPropertyTextEnum();
};
class EditorPropertyPath : public EditorProperty {