I was put under for wisdom tooth removal (wasn’t complicated, but small military clinic things differently than civilian hospitals)
I remember seeing the iv go in the waking up to being told to breath. (Side-effect of the anesthesia, not scary in the moment, but you do need to consciously breathe). I regained memory right away. I got up after I was cleared, about 20 minutes. My legs were a bit noodly. I walked out to the car and talked with my dad all the way back.
Your might be different because I’m am young and quite healthy. But my advice is to try not to panic. It makes it easier for everyone involved, and if you die to some freak accident, you die in peace :)