I made some other tests in order to verify if radiofrequency emissions affect the multimeter used.
First (minute 00:00), I tried adding another (not so good) multimeter to see if the battery voltage oscillated wildly also with it. It seems this was the case. In this test the instruments were about one meter away from the jar.
Then (00:58), I tried placing the multimeter-clampmeter without cables close to the jar, and I got disturbances in the order of hundreds of millivolts.
Finally (01:27), I added back the cables, but did not connect them to anything. I then got apparent voltage spikes even above 200V. It would seem that the cables are acting like some kind of antenna, and a more or less large part of the previously observed disturbances could be due to this.
In these tests I used newly-prepared electrolyte solution, but I inadvertently added more water than usual, and the electrolyte concentration ended up being lower than in earlier tests. Because of this, the voltage effect seen was in turn also lower than usual. Even so, it was large enough to be measured.