### 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)

s->call("set_instance_base_type", get_edited_object()->get_class());
	}
	
	Ref<ViewportTexture> vpt = p_resource;
	if (vpt.is_valid()) {
		r = Object::cast_to<Resource>(get_edited_object());
		if (r && r->get_path().is_resource_file()) {
			EditorNode::get_singleton()->show_warning(TTR("Can't create a ViewportTexture on resources saved as a file.\nResource needs to belong to a scene."));
			emit_changed(get_edited_property(), Ref<Resource>());
			update_property();
			return;
		}
		if (r && !r->is_local_to_scene()) {
			EditorNode::get_singleton()->show_warning(TTR("Can't create a ViewportTexture on this resource because it's not set as local to scene.\nPlease switch on the 'local to scene' property on it (and all resources containing it up to a node)."));
			emit_changed(get_edited_property(), Ref<Resource>());
			update_property();
			return;
		}
	}
	emit_changed(get_edited_property(), p_resource);
	update_property();
	if (is_script) {
		
		InspectorDock::get_singleton()->apply_script_properties(get_edited_object());
	}
	
	if (vpt.is_valid() && vpt->get_viewport_path_in_scene().is_empty()) {
		if (!scene_tree) {
			scene_tree = memnew(SceneTreeDialog);
			scene_tree->set_title(TTR("Pick a Viewport"));