### 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
FILTER_BY_TYPE = 64, 
		FILTER_BY_GROUP,
	};
	LineEdit *filter = nullptr;
	PopupMenu *filter_quick_menu = nullptr;
	TextureRect *filter_icon = nullptr;
	PopupMenu *menu = nullptr;
	PopupMenu *menu_subresources = nullptr;
	PopupMenu *menu_properties = nullptr;
	ConfirmationDialog *clear_inherit_confirm = nullptr;
	bool first_enter = true;
	void _create();
	void _do_create(Node *p_parent);
	Node *scene_root = nullptr;
	Node *edited_scene = nullptr;
	Node *pending_click_select = nullptr;
	bool tree_clicked = false;
	VBoxContainer *create_root_dialog = nullptr;
	String selected_favorite_root;
	Ref<ShaderMaterial> selected_shader_material;
	void _add_children_to_popup(Object *p_obj, int p_depth);
	void _node_reparent(NodePath p_path, bool p_keep_global_xform);
	void _do_reparent(Node *p_new_parent, int p_position_in_parent, Vector<Node *> p_nodes, bool p_keep_global_xform);
	void _set_owners(Node *p_owner, const Array &p_nodes);
	enum ReplaceOwnerMode {