### 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
Node *n = p_node;
	Node *newnode = p_by_node;
	if (p_keep_properties) {
		Node *default_oldnode = Object::cast_to<Node>(ClassDB::instantiate(n->get_class()));
		List<PropertyInfo> pinfo;
		n->get_property_list(&pinfo);
		for (const PropertyInfo &E : pinfo) {
			if (!(E.usage & PROPERTY_USAGE_STORAGE)) {
				continue;
			}
			if (default_oldnode->get(E.name) != n->get(E.name)) {
				newnode->set(E.name, n->get(E.name));
			}
		}
		memdelete(default_oldnode);
	}
	_push_item(nullptr);
	
	List<MethodInfo> sl;
	n->get_signal_list(&sl);
	for (const MethodInfo &E : sl) {
		List<Object::Connection> cl;
		n->get_signal_connection_list(E.name, &cl);
		for (const Object::Connection &c : cl) {
			if (!(c.flags & Object::CONNECT_PERSIST)) {
				continue;
			}
			newnode->connect(c.signal.get_name(), c.callable, Object::CONNECT_PERSIST);