Bad customer service

To provide another perspective. I'm just a person with decades of experience repairing and supporting our organization's thousands of computers of all sorts.

FYI, it is not unusual for a tech to do that in order to confirm what may be causing the problem or to look for cracks and signs of possible accidental damage. It is unfortunate the problem got worse, but more than likely that was going to happen anyway. If a tech touching the screen like that made the problem worse, then just opening & closing the lid, or carrying the laptop would likely cause that to happen anyway. There is nothing nefarious going on here as the Display already had a failure, although it is unfortunate the issue worsened.

In my own personal experience, issues with lines on the display almost always get worse on their own.

These are fellow user supported communities that are not associated with Apple Service or the retail stores. If there is another Apple Store, or Apple Authorized Service Center available to you, then give them a try without bringing up anything about the previous experience. Checking any attitude at the door may go a long way toward solving your hardware issues, and you may still be told to purchase another Mac if the actual repair costs are better spent in that manner.