I killed a pit bull once. And a couple other breeds too, over the years. I lived on the family farm out in the sticks. People would drop them out there. They would mess with the cows and that was a death sentence for them. I lived too far out to rehome or take them to a shelter. I took them out. I have never once felt bad about it.
You did what had to be done.
That’s a sad story. Sorry you had to do that.