### 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
Button *button_ui = nullptr;
	Button *button_custom = nullptr;
	Button *button_clipboard = nullptr;
	HBoxContainer *button_hb = nullptr;
	Button *edit_local, *edit_remote;
	SceneTreeEditor *scene_tree = nullptr;
	Control *remote_tree = nullptr;
	HBoxContainer *tool_hbc = nullptr;
	void _tool_selected(int p_tool, bool p_confirm_override = false);
	void _property_selected(int p_idx);
	Node *property_drop_node = nullptr;
	String resource_drop_path;
	void _perform_property_drop(Node *p_node, String p_property, Ref<Resource> p_res);
	EditorData *editor_data = nullptr;
	EditorSelection *editor_selection = nullptr;
	List<Node *> node_clipboard;
	String clipboard_source_scene;
	HashMap<String, HashMap<Ref<Resource>, Ref<Resource>>> clipboard_resource_remap;
	ScriptCreateDialog *script_create_dialog = nullptr;
	ShaderCreateDialog *shader_create_dialog = nullptr;
	AcceptDialog *accept = nullptr;
	ConfirmationDialog *delete_dialog = nullptr;
	Label *delete_dialog_label = nullptr;
	CheckBox *delete_tracks_checkbox = nullptr;
	ConfirmationDialog *editable_instance_remove_dialog = nullptr;
	ConfirmationDialog *placeholder_editable_instance_remove_dialog = nullptr;
	ReparentDialog *reparent_dialog = nullptr;
	EditorQuickOpen *quick_open = nullptr;
	EditorFileDialog *new_scene_from_dialog = nullptr;
	enum FilterMenuItems {