### 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 (button_3d) {
				button_3d->set_icon(get_theme_icon(SNAME("Node3D"), SNAME("EditorIcons")));
			}
			if (button_ui) {
				button_ui->set_icon(get_theme_icon(SNAME("Control"), SNAME("EditorIcons")));
			}
			if (button_custom) {
				button_custom->set_icon(get_theme_icon(SNAME("Add"), SNAME("EditorIcons")));
			}
			if (button_clipboard) {
				button_clipboard->set_icon(get_theme_icon(SNAME("ActionPaste"), SNAME("EditorIcons")));
			}
			menu_subresources->add_theme_constant_override("icon_max_width", get_theme_constant(SNAME("class_icon_size"), SNAME("Editor")));
		} break;
		case NOTIFICATION_PROCESS: {
			bool show_create_root = bool(EDITOR_GET("interface/editors/show_scene_tree_root_selection")) && get_tree()->get_edited_scene_root() == nullptr;
			if (show_create_root != create_root_dialog->is_visible_in_tree() && !remote_tree->is_visible()) {
				if (show_create_root) {
					create_root_dialog->show();
					scene_tree->hide();
				} else {
					create_root_dialog->hide();
					scene_tree->show();
				}
			}
		} break;
	}
}
void SceneTreeDock::_node_replace_owner(Node *p_base, Node *p_node, Node *p_root, ReplaceOwnerMode p_mode) {