### 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)

if (ps->has_connection(signal_from, c.signal.get_name(), signal_to, base_callable.get_method())) {
						exists = true;
						break;
					}
				}
				if (common_parent == p_owner) {
					break;
				} else {
					common_parent = common_parent->get_owner();
				}
			}
			if (exists) { 
				continue;
			}
			{
				Node *nl = p_node;
				bool exists2 = false;
				while (nl) {
					if (nl == p_owner) {
						Ref<SceneState> state = nl->get_scene_inherited_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;
								}
							}