### 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
new_scene_from_dialog->connect("file_selected", callable_mp(this, &SceneTreeDock::_new_scene_from));
	menu = memnew(PopupMenu);
	add_child(menu);
	menu->connect("id_pressed", callable_mp(this, &SceneTreeDock::_tool_selected).bind(false));
	menu_subresources = memnew(PopupMenu);
	menu_subresources->set_name("Sub-Resources");
	menu_subresources->connect("id_pressed", callable_mp(this, &SceneTreeDock::_tool_selected).bind(false));
	menu->add_child(menu_subresources);
	menu_properties = memnew(PopupMenu);
	add_child(menu_properties);
	menu_properties->connect("id_pressed", callable_mp(this, &SceneTreeDock::_property_selected));
	clear_inherit_confirm = memnew(ConfirmationDialog);
	clear_inherit_confirm->set_text(TTR("Clear Inheritance? (No Undo!)"));
	clear_inherit_confirm->set_ok_button_text(TTR("Clear"));
	add_child(clear_inherit_confirm);
	set_process_input(true);
	set_process(true);
	EDITOR_DEF("interface/editors/show_scene_tree_root_selection", true);
	EDITOR_DEF("interface/editors/derive_script_globals_by_name", true);
	EDITOR_DEF("docks/scene_tree/ask_before_deleting_related_animation_tracks", true);
	EDITOR_DEF("_use_favorites_root_selection", false);
	Resource::_update_configuration_warning = _update_configuration_warning;
}
SceneTreeDock::~SceneTreeDock() {
	singleton = nullptr;
	if (!node_clipboard.is_empty()) {
		_clear_clipboard();
	}
}