### 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 *p = p_desired_node;
	bool result = false;
	Vector<Node *> instances;
	while (true) {
		if (p->get_scene_file_path() == p_target_scene_path) {
			result = true;
			break;
		}
		Ref<SceneState> ss = p->get_scene_inherited_state();
		if (ss.is_valid()) {
			String path = ss->get_path();
			Ref<PackedScene> pack_data = ResourceLoader::load(path);
			if (pack_data.is_valid()) {
				p = pack_data->instantiate(PackedScene::GEN_EDIT_STATE_INSTANCE);
				if (!p) {
					continue;
				}
				instances.push_back(p);
			} else {
				break;
			}
		} else {
			break;
		}
	}