### 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
ERR_FAIL_COND(!obj);
				_push_item(obj);
			}
		}
	}
}
void SceneTreeDock::_property_selected(int p_idx) {
	ERR_FAIL_NULL(property_drop_node);
	_perform_property_drop(property_drop_node, menu_properties->get_item_metadata(p_idx), ResourceLoader::load(resource_drop_path));
	property_drop_node = nullptr;
}
void SceneTreeDock::_perform_property_drop(Node *p_node, String p_property, Ref<Resource> p_res) {
	EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
	undo_redo->create_action(vformat(TTR("Set %s"), p_property));
	undo_redo->add_do_property(p_node, p_property, p_res);
	undo_redo->add_undo_property(p_node, p_property, p_node->get(p_property));
	undo_redo->commit_action();
}
void SceneTreeDock::add_root_node(Node *p_node) {
	EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
	undo_redo->create_action_for_history(TTR("New Scene Root"), editor_data->get_current_edited_scene_history_id());
	undo_redo->add_do_method(EditorNode::get_singleton(), "set_edited_scene", p_node);
	undo_redo->add_do_method(scene_tree, "update_tree");
	undo_redo->add_do_reference(p_node);
	undo_redo->add_undo_method(EditorNode::get_singleton(), "set_edited_scene", (Object *)nullptr);
	undo_redo->commit_action();
}
void SceneTreeDock::_notification(int p_what) {
	switch (p_what) {
		case NOTIFICATION_READY: {