### 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
case TOOL_SCENE_MAKE_LOCAL: {
			if (!profile_allow_editing) {
				break;
			}
			List<Node *> selection = editor_selection->get_selected_node_list();
			List<Node *>::Element *e = selection.front();
			if (e) {
				Node *node = e->get();
				if (node) {
					Node *root = EditorNode::get_singleton()->get_edited_scene();
					EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
					if (!root) {
						break;
					}
					ERR_FAIL_COND(node->get_scene_file_path().is_empty());
					undo_redo->create_action(TTR("Make Local"));
					undo_redo->add_do_method(node, "set_scene_file_path", "");
					undo_redo->add_undo_method(node, "set_scene_file_path", node->get_scene_file_path());
					_node_replace_owner(node, node, root);
					undo_redo->add_do_method(scene_tree, "update_tree");
					undo_redo->add_undo_method(scene_tree, "update_tree");
					undo_redo->commit_action();
				}
			}
		} break;
		case TOOL_SCENE_OPEN: {
			List<Node *> selection = editor_selection->get_selected_node_list();
			List<Node *>::Element *e = selection.front();
			if (e) {
				Node *node = e->get();