### 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 (p_node != p_owner && p_node->get_owner() != p_owner && !p_owner->is_editable_instance(p_node->get_owner())) {
		return OK;
	}
	bool is_editable_instance = false;
	
	
	if (p_node != p_owner && !p_node->get_scene_file_path().is_empty() && p_owner->is_editable_instance(p_node)) {
		editable_instances.push_back(p_owner->get_path_to(p_node));
		
		is_editable_instance = true;
	} else if (p_node->get_owner() && p_owner->is_ancestor_of(p_node->get_owner()) && p_owner->is_editable_instance(p_node->get_owner())) {
		
		is_editable_instance = true;
	}
	NodeData nd;
	nd.name = _nm_get_string(p_node->get_name(), name_map);
	nd.instance = -1; 
	
	if (p_owner->get_scene_inherited_state().is_null() && (p_node == p_owner || (p_node->get_owner() == p_owner && (p_node->get_parent() == p_owner || p_node->get_parent()->get_owner() == p_owner)))) {
		
		nd.index = -1;
	} else if (p_node == p_owner) {