Sorry if this has already been covered, but do you have in writing somewhere that you were paying for the repair under duress, and intended to seek a full refund due to your travel situation and the evidence you have that shows the damage was caused in their care? This may mean nothing to the service centre staff, but will to someone who can escalate or deal with the complaint at a high enough level. Don't bother with anything legal until you've exhausted all efforts with Tesla management. If you show you mean business and present all of the images and the above info I don't think you'll find it too hard to get your money back. Make sure you don't scrub the metadata from the images.
I don't think it's uncommon generally, but this is a really bad example of a garage trying to use your situation as leverage to achieve an outcome preferable to them. Just a terrible thing to do, but I bet they've done it before and if 2 or 3 customers out of 4 just cave under pressure, they'll continue to.
The thing about employee wages is bunkum, not your fault. They will have insurance for this kind of thing or an internal policy for writing off the broken screen as a loss. I highly doubt the breakage is coming out of anyones pay, but maybe some other kind of HR action would take place. Long story short, someone messed up and they just didn't want to own up to their mistake.
So frustrating when you put your car in the care of a supposedly reputable repairer and it comes back worse or devalued in some way - been there. Especially stressful when you're hundreds of miles from home unless you have an endless pot of gold.