So this turned out to be the harbinger of a pretty serious problem. It kept getting worse, so I had to seek some real help.
Some background: I had my previous machine, a Quickmill Anita, for 16 years, and had to scrub out the grouphead brass bits a few times due to scale buildup. I had asked the great Chris Coffee support team about descaling, and they recommended never to do that because it would likely lead to more issues than it would love. Something akin to breaking off a bit of blood clot in your veins, causing a stroke. When @DavecUK recommended regular descaling for Vesuvius, I decided to ignore this piece of advice.
So I checked Vesuvius’s grouphead, and there was no scale buildup at all.
Vesuvius, however, has another valve system located just behind the grouphead (between the grouphead and the boilers, in an impossible-to-reach-yourself location). The Chris Coffee support team believed that I was getting scaling in there and would need to try descaling. Gulp. I did it, and my machine got a little worse. I did it again, and my poor Vesuvius got a stroke and pretty much completely stopped being able to either pull water through the grouphead or even refill the steam boiler. Crap.
Figuring that I needed to take apart and clean the valve system by hand, I took the panels and frame off the machine and discovered how completely screwed I was. I was going to have to remove both boilers, and a majority of the electronics to get anywhere near this valve system. And when I tried to do that, I discovered that the system was put together and sealed so tightly that I was likely to break a pipe before the nuts holding the piping to the boilers would loosen. Oh, and you can’t ship this thing anywhere for repairs; it’s too big.
I thought about trying to find a place to repair it, but the one in the SF Bay Area was so busy with commercial work that they couldn’t even get me on their calendar.
So my Vesuvius sat there. Full of vinegar. And after 2 months like that, the valve system descaled. I flushed it out with water for 2 days, and it seems to be working fine again.
Moral of the story: when @DavecUK recommends frequent descaling, listen!