Sure, it is a strange experience especially if you have never been sedated. (I have had one surgery under full anesthesia as a child, not that I remember much of it.) But it is completely routine and very brief - 30 minutes or so.
Is it just the psychological discomfort about something you are unfamiliar with, or are there other specific worries you have (for example, regarding your BG in the meantime)? I had my husband in the main exam room until they took me over to the “mini-OR” where the retrieval took place and that gave me comfort. If I remember correctly, I chose to take off my pump during the procedure (I can easily go up to an hour off without major impact to my BG, but I know this is not the same for everyone) and didn’t wear a sensor so that there were no alarms, etc. that someone else might have to deal with while I was under. It is truly painless and in my case I didn’t have any strong discomfort afterward either. Obviously I measured as I was going in to make sure I was at a good level and then had my husband measure me as soon as I came out (I was a little drowsy for a while). His memory is that I was a little low, something in the 70s so I didn’t even connect back until a little later still, but I don’t remember those details. I think we left about 30 minutes after the procedure finished when it seemed I was feeling fine. But I think they would have let me stay in the clinic as long as I needed to to recover.
(Our retrieval and transfer were performed in a town about 2.5 hours away from where we live and after the retrieval we went shopping at Whole Foods, which we don’t have where we live , and then drove back.)
I would recommend you try to figure out what specifically provokes your anxiety and then plan comfort measures that will help you deal with it.