### 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)

label = memnew(Label);
	add_child(label);
}
void EditorPropertyResource::_set_read_only(bool p_read_only) {
	resource_picker->set_editable(!p_read_only);
}
void EditorPropertyResource::_resource_selected(const Ref<Resource> &p_resource, bool p_inspect) {
	if (p_resource->is_built_in() && !p_resource->get_path().is_empty()) {
		String parent = p_resource->get_path().get_slice("::", 0);
		List<String> extensions;
		ResourceLoader::get_recognized_extensions_for_type("PackedScene", &extensions);
		if (p_inspect) {
			if (extensions.find(parent.get_extension()) && (!EditorNode::get_singleton()->get_edited_scene() || EditorNode::get_singleton()->get_edited_scene()->get_scene_file_path() != parent)) {
				
				if (!FileAccess::exists(parent + ".import")) {
					EditorNode::get_singleton()->call_deferred("edit_foreign_resource", p_resource);
					return;
				}
			}
		}
	}
	if (!p_inspect && use_sub_inspector) {
		bool unfold = !get_edited_object()->editor_is_section_unfolded(get_edited_property());
		get_edited_object()->editor_set_section_unfold(get_edited_property(), unfold);
		update_property();
	} else {
		emit_signal(SNAME("resource_selected"), get_edited_property(), p_resource);
	}
}
static bool _find_recursive_resources(const Variant &v, HashSet<Resource *> &resources_found) {