I was right about motivation from the updating of the project logs — right after I finished the last log, I decided to continue the exploration. So I took a piece of paper and I figured out which pin is connected to which pad:
Then I connected the power to the VCC and GND pins, and measured the voltages against GND and against VCC on all pins, hoping that maybe this will give me some insights. The results are a little bit weird, so I decided to also try and measure the resistance between all pins and VCC and GND — of course with the power disconnected.
The results were even stranger, so I repeated the same procedure with the second module, and got completely different results.
My suspicion so far is that it's indeed very hard to get those pads soldered properly without shorts and breaks, and that I did a poor job with it.