So, this may come down to how much are YOU paying for this? If your deductible is, as an example, $500 then you are out $500 either way unless you are trying to avoid a claim and pay out of pocket. Either shop may very well end up resulting in a Carfax blemish (which, sadly, will cost you more than this accident at resale).
As to the actual repair, I am guessing that EITHER shop will do the same thing:
Bumper
- remove
- repair scratches/scuffs
- sand/prime/paint
- reinstall bumper
Quarter Panel
- pull any dents
- fill
- sand / prime / paint (note: likely the whole quarter)
Replacing the bumper would appear to be overkill (basically it always comes down to how bad the damage is to the bumper and the cost of a replacement bumper - i.e. labor/damage/part cost). The quarter damage is mild (based on what we see here) and would just be pulled/filled w/o any metal welding or bonding work).
Unless the cheaper shop is "shady" or "low rent" (i.e. make sure they understand the need to paint match or blend...although "black" should be more straightforward) if it is apples/apples work the cheaper shops rate is reasonable AND you are paying out of pocket, then they are worth choosing. If the insurance is paying, then, in order to avoid any hassles later on with Tesla themselves (i.e. oops, we need a part) then maybe you just go with the "approved" shop.
There's nothing Tesla-specific or magic here other than Tesla's unfortunate limited repair shop policy...