Sorry for your loss, but glad everyone is ok, just be sure your wife goes to the hospital for a full exam, since alot of potential damage can't/won't be discovered by EMT's & their limited equipment/skills at the scene....
If the accident was/is determined to be the other driver's fault (??), they will be responsible not only for the vehicle & property damage, but also all medical expenses...
As for the vehicle, based on those 2 pics, it may be repairable, provided the frame was not bent, and the drive train is ok, and everything else can be fixed without too much trouble...
You may already know this, but in the last few years, a lot of insurance companies seem to be more likely to total out most vehicles rather than authorizing repairs, since alot of other issues can be discovered at the shop, which will add to the repair costs...
When my wife's 015 Acadia was totaled out due to an accident in '22, they gave us 2 options:
A) Take a large check and they haul it away to the junk yard, OR
B) Take a smaller check, keep the vehicle & do whatever we wanted with it.. the problem with this option is that the vehicle's title will be converted to a Salvage title, but here's the killer part: They (nor any other insurance co) will NOT provide any insurance coverage for any salvage-titled vehicles, which in my state makes it ineligible for registration & plates....so basically that would have turned it into a non-drivable hunk-o-junk for us
Needless to say we took option A
Good luck & please keep us updated