### 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
undo_redo->add_do_method(n, "set_script", empty);
					undo_redo->add_undo_method(n, "set_script", existing);
				}
			}
			undo_redo->add_do_method(this, "_update_script_button");
			undo_redo->add_undo_method(this, "_update_script_button");
			undo_redo->commit_action();
		} break;
		case TOOL_MOVE_UP:
		case TOOL_MOVE_DOWN: {
			if (!profile_allow_editing) {
				break;
			}
			if (!scene_tree->get_selected()) {
				break;
			}
			if (scene_tree->get_selected() == edited_scene) {
				current_option = -1;
				accept->set_text(TTR("This operation can't be done on the tree root."));
				accept->popup_centered();
				break;
			}
			if (!_validate_no_foreign()) {
				break;
			}
			bool MOVING_DOWN = (p_tool == TOOL_MOVE_DOWN);
			bool MOVING_UP = !MOVING_DOWN;
			Node *common_parent = scene_tree->get_selected()->get_parent();
			List<Node *> selection = editor_selection->get_selected_node_list();
			selection.sort_custom<Node::Comparator>();