Hi,
You don't need to over worry. One issue I notice in the forums is an excessive fear of anesthesia. A vet wouldn't administer anesthesia to any dog if he/she believes it posses a health risk on the dog based on pre-op tests. People here over worry about it!
It's very important that you work with a veterinarian you feel comfortable with and seems like know what's he's doing. Ask the right questions based on the anasthesia protocol posted on a threat here n YT.
Like human surgeries, anesthesia has it risks, but I think the chances of dead are very slim. Don't worry. Your pup will be fine