### Godot version

v4.1.1.stable.official [bd6af8e0e]

### System information

Godot v4.1.1.stable - Debian GNU/Linux trixie/sid trixie - Vulkan (Compatibility) - Mesa Intel(R) HD Graphics 520 (SKL GT2) () - Intel(R) Core(TM) i7-6500U CPU @ 2.50GHz (4 Threads)

### Issue description

After right clicking in thet "Filter Nodes" menu in the scene tree dock, the sub-menu is populated with a "Search" icon.

If I later switch themes in the same session, this icon is never updated to match the new theme.

![image](https://github.com/godotengine/godot/assets/660911/14336bb3-12ca-48c8-b030-8ada6ac27ec6)


### Steps to reproduce

1. Right click in the "Filter Nodes" menu in scene tree dock
2. Switch themes
3. Right click again in the "Filter Nodes" menu

Expected result: Icon has updated to match the theme I am currently using
Actual result: Icon is still using the theme I launched Godot with

### Minimal reproduction project

N/A
if (scene->get_scene_inherited_state().is_valid() && scene->get_scene_inherited_state()->find_node_by_path(scene->get_path_to(tocopy)) >= 0) {
				accept->set_text(TTR("Can't save a branch which is part of an inherited scene.\nTo save this branch into its own scene, open the original scene, right click on this branch, and select \"Save Branch as Scene\"."));
				accept->popup_centered();
				break;
			}
			new_scene_from_dialog->set_file_mode(EditorFileDialog::FILE_MODE_SAVE_FILE);
			List<String> extensions;
			Ref<PackedScene> sd = memnew(PackedScene);
			ResourceSaver::get_recognized_extensions(sd, &extensions);
			new_scene_from_dialog->clear_filters();
			for (int i = 0; i < extensions.size(); i++) {
				new_scene_from_dialog->add_filter("*." + extensions[i], extensions[i].to_upper());
			}
			String existing;
			if (extensions.size()) {
				String root_name(tocopy->get_name());
				root_name = EditorNode::adjust_scene_name_casing(root_name);
				existing = root_name + "." + extensions.front()->get().to_lower();
			}
			new_scene_from_dialog->set_current_path(existing);
			new_scene_from_dialog->set_title(TTR("Save New Scene As..."));
			new_scene_from_dialog->popup_file_dialog();
		} break;
		case TOOL_COPY_NODE_PATH: {
			List<Node *> selection = editor_selection->get_selected_node_list();
			List<Node *>::Element *e = selection.front();
			if (e) {
				Node *node = e->get();
				if (node) {
					Node *root = EditorNode::get_singleton()->get_edited_scene();