### 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)

List<Pair<StringName, Variant>> old_state;
						if (node->get_script_instance()) {
							node->get_script_instance()->get_property_state(old_state);
						}
						node->set(snames[nprops[j].name], props[nprops[j].value], &valid);
						
						for (const Pair<StringName, Variant> &E : old_state) {
							node->set(E.first, E.second);
						}
					} else {
						Variant value = props[nprops[j].value];
						if (value.get_type() == Variant::OBJECT) {
							
							Ref<Resource> res = value;
							if (res.is_valid()) {
								if (res->is_local_to_scene()) {
									
									
									
									
									
									
									
									if (n.instance >= 0) {
										Ref<Resource> node_res = node->get(snames[nprops[j].name]);
										if (node_res.is_valid()) {
											node_res->copy_from(res);
											node_res->configure_for_local_scene(node, resources_local_to_scene);
											value = node_res;