Well, I figured it out.
The manual says to use 12 liters of mash water, so that's what I started with. It seemed crazy, but what do I know? First time with an AIO. Those clever Germans! They figured out a way to mash with less water!
I could tell the Braumeister's bottom was going dry, so I added more.
After I finished brewing, I took the neoprene jacket off and saw a burned place.
Then I looked at the manual again. It says to use 12 liters for the 10L model and 23 liters for the 20L. I actually checked it more than once before mashing, and I still did not notice this.
I guess this explains the low OG. I happened to have a tiny amount of DME on hand, so I dumped that in, and I got to 1.054 if I am using the refractometer correctly. For a while, it looked like I was going to be at 1.040. I was shooting for 1.056.
The jacket got burned because there wasn't always enough water in the machine.
Anyway, the beer should be okay, if not absolutely perfect, and that's a win in my book, after 16 years of brewing nothing.