### 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 (is_read_only()) {
		return false;
	}
	String allowed_type = Variant::get_type_name(subtype);
	
	
	if (subtype == Variant::OBJECT && !subtype_hint_string.is_empty()) {
		allowed_type = subtype_hint_string;
	}
	Dictionary drag_data = p_drag_data;
	if (drag_data.has("type") && String(drag_data["type"]) == "files") {
		Vector<String> files = drag_data["files"];
		for (int i = 0; i < files.size(); i++) {
			String file = files[i];
			String ftype = EditorFileSystem::get_singleton()->get_file_type(file);
			for (int j = 0; j < allowed_type.get_slice_count(","); j++) {
				String at = allowed_type.get_slice(",", j).strip_edges();
				
				if (!ClassDB::is_parent_class(ftype, at)) {
					return false;
				}
			}
		}
		
		return true;
	}
	return false;
}
bool EditorPropertyArray::can_drop_data_fw(const Point2 &p_point, const Variant &p_data, Control *p_from) const {