The green circle highlights the hole that formed in the pipe that feeds cold water into the tank.
It appears that we hadn't released enough hot water from the tank, so even though we'd shut off the feed, water was coming out the hole, albeit much more slowly than yesterday. This time no water had gotten into the carpet, just the overflow pan. We left the hot water tap in the bathroom on to release pressure, and Lisa had us get the garden hose and attach it to the drain.
Draining the tank at least enough to release pressure was challenging because the hose had to stretch all the way across the living room and to the front walk. In fact, water didn't come out the other end until after we disconnected it from the drain valve (after guessing that some water had drained), then lifted the end up and walked it across the room to the front door.
We were not pleased with the rusty look of the water coming out of the hose. By our thinking, there shouldn't be that much build-up in the tank already. Worse, after mopping up the water in the overflow pan, more water (not a lot) continued to appear. This makes us worry that there might be something more serious than just the small hole in the feed line. The water heater is just a few days short of two years old and has given good service so far.
Because of the concerns over additional leakage, Lisa decided that we can't risk trying to patch the hole temporarily and re-pressurize the tank. We left a message with our plumber's answering service, explaining that it's not an emergency, but it is something that needs to be addressed as soon as possible on Monday during normal working hours if possible.