### 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<Node::GroupInfo> groups;
	p_node->get_groups(&groups);
	for (const Node::GroupInfo &gi : groups) {
		if (!gi.persistent) {
			continue;
		}
		bool skip = false;
		for (const SceneState::PackState &ia : states_stack) {
			
			if (ia.state->is_node_in_group(ia.node, gi.name)) {
				skip = true;
				break;
			}
		}
		if (skip) {
			continue;
		}
		nd.groups.push_back(_nm_get_string(gi.name, name_map));
	}
	
	
	
	
	if (p_node == p_owner) {
		
		nd.owner = -1;
	} else if (p_node->get_owner() == p_owner) {