### 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
if (selection.size() == 1) {
		bool is_external = (!selection[0]->get_scene_file_path().is_empty());
		if (is_external) {
			bool is_inherited = selection[0]->get_scene_inherited_state() != nullptr;
			bool is_top_level = selection[0]->get_owner() == nullptr;
			if (is_inherited && is_top_level) {
				menu->add_separator();
				if (profile_allow_editing) {
					menu->add_item(TTR("Clear Inheritance"), TOOL_SCENE_CLEAR_INHERITANCE);
				}
				menu->add_icon_item(get_theme_icon(SNAME("Load"), SNAME("EditorIcons")), TTR("Open in Editor"), TOOL_SCENE_OPEN_INHERITED);
			} else if (!is_top_level) {
				menu->add_separator();
				bool editable = EditorNode::get_singleton()->get_edited_scene()->is_editable_instance(selection[0]);
				bool placeholder = selection[0]->get_scene_instance_load_placeholder();
				if (profile_allow_editing) {
					menu->add_check_item(TTR("Editable Children"), TOOL_SCENE_EDITABLE_CHILDREN);
					menu->add_check_item(TTR("Load As Placeholder"), TOOL_SCENE_USE_PLACEHOLDER);
					menu->add_item(TTR("Make Local"), TOOL_SCENE_MAKE_LOCAL);
				}
				menu->add_icon_item(get_theme_icon(SNAME("Load"), SNAME("EditorIcons")), TTR("Open in Editor"), TOOL_SCENE_OPEN);
				if (profile_allow_editing) {
					menu->set_item_checked(menu->get_item_idx_from_text(TTR("Editable Children")), editable);
					menu->set_item_checked(menu->get_item_idx_from_text(TTR("Load As Placeholder")), placeholder);
				}
			}
		}
	}
#ifdef MODULE_REGEX_ENABLED
	if (profile_allow_editing && selection.size() > 1) {