Oh my....my heart aches for you so badly. I read your story and felt like I was there. You did the best you could, don't beat yourself up. Accidents happen, and it was a tragic accident. I know many people arent aware, but a cat has a chemical in its saliva and claws that are toxic to birds and rodents. It won't kill it immediately, but over a short period of time, it will kill them. It can happen from a bite or a scratch. That may be the case here. I'm not a vet, but I know this for a fact.
That is why many people say, "cat scratch fever" , a human actually will itch in the spot when you get scratched by a cat.
My prayers to ease your pain are being said tonight. I am glad the suffering for Jas was short. He knows you loved him.
Time will lessen the pain, be patient and forgiving of yourself.