I do understand that, yeah. And thanks for the neat analogy.
What I believe is, you probably won't actually ever have to stop drinking wine. From your perspective, I'm not sure it's meaningful to say you'll ever stop existing, because you can't experience it. You'll (probably) just stop existing for me, and I for you.
It's fair to be sad about it just like I'm sad that the elves left Middle Earth at the end of the Third Age. But neither my own death nor the leaving of the elves is something I can ever actually live through - they're both just stories to me.
I’m not worried about the nothingness after I die. I’m anxious about the impending loss of enjoying my wine.
Have you ever been to a party and it started winding down and people left and you wanted them to stay and the fun to continue? That’s the anxiety.