### 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)

base_node = Object::cast_to<Node>(get_edited_object());
		if (!base_node) {
			
			if (EditorNode::get_singleton()->get_editor_selection_history()->get_path_size() > 0) {
				Object *base = ObjectDB::get_instance(EditorNode::get_singleton()->get_editor_selection_history()->get_path_object(0));
				if (base) {
					base_node = Object::cast_to<Node>(base);
				}
			}
		}
	}
	if (!base_node && get_edited_object()->has_method("get_root_path")) {
		base_node = Object::cast_to<Node>(get_edited_object()->call("get_root_path"));
	}
	if (!base_node && Object::cast_to<RefCounted>(get_edited_object())) {
		Node *to_node = get_node(p_path);
		ERR_FAIL_COND(!to_node);
		path = get_tree()->get_edited_scene_root()->get_path_to(to_node);
	}
	if (base_node) { 
		path = base_node->get_path().rel_path_to(p_path);
	}
	if (pointer_mode && base_node) {
		emit_changed(_get_meta_pointer_property(), path);
	} else {
		emit_changed(get_edited_property(), path);
	}
	update_property();
}
void EditorPropertyNodePath::_node_assign() {