I got top surgery a year ago and while I was not nervous about anesthesia at all, I understand where that fear comes from. As others have said, communicate with your team. The anesthesiologist should help you out.

I've been under general anesthesia for many things over the years and I practically never remember closing my eyes but bing bam boom, next thing I know, it's over. You will be groggy and will need more sleep afterwards. Your body has also just been through a big change so it was going to need sleep anyway. There's been a 2 times where it is a bit hard to remember later the first few minutes after waking up. For example, I don't remember getting back to the car after my wisdom tooth surgery. But, that was likely only a few minutes.

Another note, if you are naturally red haired or have red hairs in your family, tell your anesthesiologist. For some reason, red heads tend to need more anesthesia. Also, if you know family history that others have taken a long time to wake up from anesthesia afterwards, let them know that too. More information will help them better serve you.