### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
Node *selected_node = nullptr;
		if (current_obj->is_class("MultiNodeEdit")) {
			Node *scene = get_edited_scene();
			if (scene) {
				MultiNodeEdit *multi_node_edit = Object::cast_to<MultiNodeEdit>(current_obj);
				int node_count = multi_node_edit->get_node_count();
				if (node_count > 0) {
					List<Node *> multi_nodes;
					for (int node_index = 0; node_index < node_count; ++node_index) {
						Node *node = scene->get_node(multi_node_edit->get_node(node_index));
						if (node) {
							multi_nodes.push_back(node);
						}
					}
					if (!multi_nodes.is_empty()) {
						
						multi_nodes.sort_custom<Node::Comparator>();
						selected_node = multi_nodes.front()->get();
					}
				}
			}
		}
		InspectorDock::get_inspector_singleton()->edit(current_obj);
		NodeDock::get_singleton()->set_node(nullptr);
		SceneTreeDock::get_singleton()->set_selected(selected_node);
		InspectorDock::get_singleton()->update(nullptr);
	}
	InspectorDock::get_singleton()->set_info(
			info_is_warning ? TTR("Changes may be lost!") : TTR("This object is read-only."),
			editable_info,