I had an extended loss of power during Hurricane Beryl 7/2024 and purchased a generator. Can I deduct the generator's cost since it was a federal disaster area?

No.  The purchase of a generator would not be considered a loss. A loss would be if you already had the generator and it was destroyed during the hurricane.   If you lost the food, you would be able to claim the loss of the food, but you cannot claim an upgrade as a loss.