Losing cursor in build, works OK in Play Mode

I am going through the usual n00by struggles, trying to get a grip on Unity. I have created a very tiny 3d fps game, one scene plus a simple user menu. Within Unity I can:

   - enter Play Mode, see scene 0 (menu screen)
   - click on Start button, switch to scene 1 (3d game scene)
   - play game in Play Mode, walk around, etc
   - press ESC to return to menu (scene 0)
   - click on Quit button to quit to 3d Editor Mode

All of this works perfectly and I'm pretty chuffed. Now I do a Build (to Mac/OSX) and run the resulting .app -- and this is what happens:

   - on startup, get correct menu screen (scene 0) and mouse cursor
   - press Start button, enter game
   - play game, walk around, etc
   - press ESC, return to menu screen
   - OOPS -- no cursor.  I can't exit the game!  I have to kill it from the OS.

I thought that Play Mode should accurately reflect what would happen in the build. What have I done wrong? My cursor-preserving code on exiting play mode is

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 using UnityEngine.SceneManagement;
 
 public class EscapeToMenu : MonoBehaviour {
 
     public void LoadByIndex(int sceneIndex)
     {
         SceneManager.LoadScene(sceneIndex);
     }
 
     void Update()
     {
         if (Input.GetKey(KeyCode.Escape))
         {
             LoadByIndex(0);
             Cursor.visible = true;
         }
     }
 
 }

For all I know this is a very stupid way to do this, but I'm very new (been using Unity about 2 days now). On ESC I load Scene 0, the menu screen, and then I tell the cursor to be visible (it becomes invisible in Play Mode). I've clearly missed an important step -- the build is not working the same as the Play Mode, Scene 0 is losing its cursor after 3d activity in Scene 1 -- can someone please unconfuse me?

[UPDATE] Finally I found the answer, after much googling and headbanging. I needed one more line of code in my Update function:

         Screen.lockCursor = false;

This is the secret! The cursor is now usable after exiting to the menu screen.