### 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)

return _is_drop_valid(p_data);
}
void EditorPropertyArray::drop_data_fw(const Point2 &p_point, const Variant &p_data, Control *p_from) {
	ERR_FAIL_COND(!_is_drop_valid(p_data));
	Dictionary drag_data = p_data;
	if (drag_data.has("type") && String(drag_data["type"]) == "files") {
		Vector<String> files = drag_data["files"];
		Variant array = object->get_array();
		
		if (!array.is_array()) {
			initialize_array(array);
		} else {
			array = array.duplicate();
		}
		
		for (int i = 0; i < files.size(); i++) {
			String file = files[i];
			Ref<Resource> res = ResourceLoader::load(file);
			if (res.is_valid()) {
				array.call("push_back", res);
			}
		}
		emit_changed(get_edited_property(), array, "", false);
		update_property();
	}
}
void EditorPropertyArray::_notification(int p_what) {