Since you asked for others perspectives, here's mine. Accidents happen. learn from it going forward.
Sorry, this was totally your fault. You were distracted, talking, listing to a radio loud enough that you did not hear the garage door lowering. Worse, you failed to ensure the area behind your car was clear before starting to back out. What if a child or animal walked behind your car? Tesla's fault if you hit them or it?
You admitted you were not watching as you backed up, then stated that it is "common" for people to drive this way. I will advise you this is not common for people to drive this way. If your car is moving in reverse, it's your responsibility to watch behind you as you are moving in reverse.
Your mirrors are angled down is your excuse for not ensuring the sides were clear enough to start backing out is a poor excuse. May I suggest you create a 'GARAGE' profile for the future, which is set to not turn your mirrors downward, and if you have garage door clearance, does not fold mirrors in, or if you do not have garage door clearance, manually fold the mirrors in as you approach the door threshold.
Expecting Tesla, or anyone else to pay for the damage is unrealistic in this case.
Edit: Enabling auto close was not a good idea in the first place, but you know that now. This is mostly for others who may have it enabled.