Prevent last updated property from changing when updating node in code?

I have this code that updates a node in a queue worker:

      $changed = $entity->getChangedTime();
      // Don't update the changed time by 
      $entity->setChangedTime($changed);
      $entity->set('my_field', "my_data");
      $entity->setNewRevision(FALSE);
      $entity->save();
      

Here is a screenshot of xdebug showing changed and after_save value with the relevant code:

But no matter what I do, the changed property keeps getting updated to the time of the update.

I tested the functionality in a different contenxt like:

  $node = Node::load($nid);
  $changed_time = new DrupalDateTime('2022-01-01 12:00:00');
  $timestamp = $changed_time->getTimestamp();
  $node->setChangedTime($timestamp);
  $node->save();

and this seem to work.

Why does my code in the queue worker fail to do the same thing? is it because it's updating a field value?

There's a module that could help with your request. It's a bit hackish but it works.