I know it says don't unplug your Studio Display, but that's not just power alone. You cannot unplug your Mac either. I had always thought it downloaded through Mac, and then moved the file over. Given the Studio Display has its own processor, etc I thought it was fully capable of updating itself.
I read the warning twice too and it basically said don't unplug your Studio Display only, which I took to mean power. Disconnecting the Mac is a no-no.
I unplugged my Mac because I was in a hurry out the door to get to the office, but I wanted to wait for it to complete. Well the second I did the update stalled. A few seconds later I got the restore screen. Going to the website doesn't do anything except tell you to reboot the display and try again.
I plugged my Mac back in and saw nothing at first. I had to hop on a call for work so I started working on that with the assumption my display was dead, but maybe 5 mintues in the call I look up and I see the update screen is back. Afterward my display came back to life.
They should make it clear do not unplug the Studio Display. Do not unplug your Mac from the Studio Display as well. I would not have unplugged if I wasn't in a rush to get out the door for work, but I think they should be more clear on this precautionary message.
Edit: I assumed this was similar to the watch update where the update gets downloaded to the display and then the display takes over the update (similar to the Watch) given they have their own processors. I guess the display probably has minimal memory/storage unlike a watch that has enough storage for apps/media too.