### 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)

}
						nl = nullptr;
					} else {
						if (!nl->get_scene_file_path().is_empty()) {
							
							Ref<SceneState> state = nl->get_scene_instance_state();
							if (state.is_valid()) {
								int from_node = state->find_node_by_path(nl->get_path_to(p_node));
								int to_node = state->find_node_by_path(nl->get_path_to(target));
								if (from_node >= 0 && to_node >= 0) {
									
									if (state->is_connection(from_node, c.signal.get_name(), to_node, base_callable.get_method())) {
										exists2 = true;
										break;
									}
								}
							}
						}
						nl = nl->get_owner();
					}
				}
				if (exists2) {
					continue;
				}
			}
			int src_id;
			if (node_map.has(p_node)) {
				src_id = node_map[p_node];
			} else {
				if (nodepath_map.has(p_node)) {