I am so very sorry to hear about your loss of Paar. It is not your fault. If it hadn’t been this time, it may have happened for some other surgery or reason due to his heart. He went peacefully, with no pain and he was oblivious to it all so he wasn’t afraid. You were doing what you and many others consider to be the best. You wanted what was best for him, and he knew that. Paar wouldn’t hold you at fault for this, and you shouldn’t either. Take your time to grieve and don’t let anyone tell you your feelings or mourning are invalid. Don’t rush yourself. Be gentle to yourself.
And yes- I’ve lost a bunny during neutering. You are not alone. Larkin passed while he was coming out of the anesthetic and his lungs failed him. I too had had a bad feeling– but it had been for his first appointment to get neutered, so I listened to it and kept him home because I figured I was picking up on him having a cold or something and wanted him to feel perfect for his big day. So I rescheduled and it was during the second appointment, when he actually went, and I had no bad feelings, and was completely confident I would be bringing him home – alive and well- in a few hours, and alas, this was not what happened.
Believe me, you will always miss your bunny, but the pain, guilt and second-guessing will ease with time. Take your time. Your bunny would want you to feel their love and appreciation for the care you provided them during their life.