### 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)

Vector<StringName> valid_types;
			valid_types.push_back("Viewport");
			scene_tree->get_scene_tree()->set_valid_types(valid_types);
			scene_tree->get_scene_tree()->set_show_enabled_subscene(true);
			add_child(scene_tree);
			scene_tree->connect("selected", callable_mp(this, &EditorPropertyResource::_viewport_selected));
		}
		scene_tree->popup_scenetree_dialog();
	}
}
void EditorPropertyResource::_sub_inspector_property_keyed(const String &p_property, const Variant &p_value, bool p_advance) {
	
	const Variant args[3] = { String(get_edited_property()) + ":" + p_property, p_value, p_advance };
	const Variant *argp[3] = { &args[0], &args[1], &args[2] };
	emit_signalp(SNAME("property_keyed_with_value"), argp, 3);
}
void EditorPropertyResource::_sub_inspector_resource_selected(const Ref<Resource> &p_resource, const String &p_property) {
	emit_signal(SNAME("resource_selected"), String(get_edited_property()) + ":" + p_property, p_resource);
}
void EditorPropertyResource::_sub_inspector_object_id_selected(int p_id) {
	emit_signal(SNAME("object_id_selected"), get_edited_property(), p_id);
}
void EditorPropertyResource::_open_editor_pressed() {
	Ref<Resource> res = get_edited_property_value();
	if (res.is_valid()) {
		
		callable_mp(EditorNode::get_singleton(), &EditorNode::edit_item).bind(res.ptr(), this).call_deferred();
	}
}
void EditorPropertyResource::_update_property_bg() {