### 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
selected_favorite_root = p_class;
	_tool_selected(TOOL_CREATE_FAVORITE);
}
void SceneTreeDock::_feature_profile_changed() {
	Ref<EditorFeatureProfile> profile = EditorFeatureProfileManager::get_singleton()->get_current_profile();
	if (profile.is_valid()) {
		profile_allow_editing = !profile->is_feature_disabled(EditorFeatureProfile::FEATURE_SCENE_TREE);
		profile_allow_script_editing = !profile->is_feature_disabled(EditorFeatureProfile::FEATURE_SCRIPT);
		bool profile_allow_3d = !profile->is_feature_disabled(EditorFeatureProfile::FEATURE_3D);
		button_3d->set_visible(profile_allow_3d);
		button_add->set_visible(profile_allow_editing);
		button_instance->set_visible(profile_allow_editing);
		scene_tree->set_can_rename(profile_allow_editing);
	} else {
		button_3d->set_visible(true);
		button_add->set_visible(true);
		button_instance->set_visible(true);
		scene_tree->set_can_rename(true);
		profile_allow_editing = true;
		profile_allow_script_editing = true;
	}
	_update_script_button();
}
void SceneTreeDock::_clear_clipboard() {