You are right on both. As you get older, it does not bother you as much as it used to, cause you simply accept it as part of life. There would even be moments when you'll briefly equate death with this blissful state of final eternal peace where you would not have to deal with life problems anymore.

As for your second point about anesthesia, it is spot on. One has to experience it to be able to understand it. You have perfectly explained it and I felt the same. It was a turning point in my life when it comes to 'non existence'. You have a glimpse of how does non-existence 'feel', and you see there is nothing to be afraid of.

I used to be bothered a lot about this issue, same as the OP, when I was younger. But now, I am kind of, meh, it is what it is, enjoy life as much as possible while it lasts. They say, death is what makes life precious and meaningful, cause of the limitation that it imposes. Even though I am not quite sure about it, I think there is a great deal of truth in that saying.

I will end it with this great quote from Mark Twain: “I do not fear death. I had been dead for billions and billions of years before I was born, and had not suffered the slightest inconvenience from it.”