### 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
MODE_BIDI,
		MODE_DO,
		MODE_UNDO
	};
	void _node_replace_owner(Node *p_base, Node *p_node, Node *p_root, ReplaceOwnerMode p_mode = MODE_BIDI);
	void _load_request(const String &p_path);
	void _script_open_request(const Ref<Script> &p_script);
	void _push_item(Object *p_object);
	void _handle_select(Node *p_node);
	bool _cyclical_dependency_exists(const String &p_target_scene_path, Node *p_desired_node);
	bool _track_inherit(const String &p_target_scene_path, Node *p_desired_node);
	void _node_selected();
	void _node_renamed();
	void _script_created(Ref<Script> p_script);
	void _shader_created(Ref<Shader> p_shader);
	void _script_creation_closed();
	void _shader_creation_closed();
	void _delete_confirm(bool p_cut = false);
	void _delete_dialog_closed();
	void _toggle_editable_children_from_selection();
	void _toggle_editable_children(Node *p_node);
	void _toggle_placeholder_from_selection();
	void _node_prerenamed(Node *p_node, const String &p_new_name);
	void _nodes_drag_begin();