My cat isn’t alive and it’s my fault

I miss my cat. At the beginning of June, she was slowing down and stopped eating so we went to the vet. They treated her and told me she was having liver failure, recommending I put her down that day. I took her home to let her die with her brother (a little dog) and to be in her own bed when the time came. She got better almost immediately. Back to her old self. But last week on Tuesday she suddenly became extremely ill. She was soiling herself and throwing up yellow foam, wouldn’t eat or drink. Her vet couldn’t get her in until the next day. She got even worse over night so in the morning before her appointment, I discussed euthanasia with the Vet over the phone. I got her carrier out and was prepping her for her journey to death, when she started licking at her food and putting her face by the water, pretending to drink it. I went through with the euthanasia anyways. I hate myself. Maybe if I let her stay home, she would have gotten better again. My brother keeps telling me I ‘made the right decision’, but who am I to decide when her life should have ended? How do I know the extent of her pain, or her wants? I held her little body in my hands when she went limp and I knew I’d never hold her again. I made the wrong decision and selected to murdered my best friend. There’s no one to talk to. I have to pick up her ashes next week. I’ve done a lot in this life that I regret, but killing my cat is the one choice I wish more than anything that I could undo. She wasn’t the first cat I’ve euthanized. This feels wrong and I can’t stop thinking about how it feels like murder rather than an act of mercy.