### 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 (ccb) {
					binds = ccb->get_binds();
					base_callable = ccb->get_callable();
				}
				CallableCustomUnbind *ccu = dynamic_cast<CallableCustomUnbind *>(c.callable.get_custom());
				if (ccu) {
					unbinds = ccu->get_unbinds();
					base_callable = ccu->get_callable();
				}
			} else {
				base_callable = c.callable;
			}
			
			Node *common_parent = target->find_common_parent_with(p_node);
			ERR_CONTINUE(!common_parent);
			if (common_parent != p_owner && common_parent->get_scene_file_path().is_empty()) {
				common_parent = common_parent->get_owner();
			}
			bool exists = false;
			
			while (common_parent) {
				Ref<SceneState> ps;
				if (common_parent == p_owner) {
					ps = common_parent->get_scene_inherited_state();
				} else {
					ps = common_parent->get_scene_instance_state();
				}
				if (ps.is_valid()) {
					NodePath signal_from = common_parent->get_path_to(p_node);
					NodePath signal_to = common_parent->get_path_to(target);