### 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)

nd.owner = 0;
	} else {
		nd.owner = -1;
	}
	MissingNode *missing_node = Object::cast_to<MissingNode>(p_node);
	
	
	if (states_stack.is_empty() && !is_editable_instance) {
		
		if (missing_node != nullptr) {
			
			nd.type = _nm_get_string(missing_node->get_original_class(), name_map);
		} else {
			nd.type = _nm_get_string(p_node->get_class(), name_map);
		}
	} else {
		
		
		nd.type = TYPE_INSTANTIATED;
	}
	
	
	
	
	
	bool save_node = nd.properties.size() || nd.groups.size(); 
	save_node = save_node || p_node == p_owner; 
	save_node = save_node || (p_node->get_owner() == p_owner && instantiated_by_owner); 
	int idx = nodes.size();