OK. I would have a lot to tell, and I would do it if this forum was in French. But I am not fluent enough in English to tell what I'd like to... And it would probably be misinterpreted.
My initial questions were:
1) Is the cell balancing occurring only during the charge of the battery, or is the BMS able to do it when the bike is resting?
2) In the case where the BMS is able to do it when the bike is resting, of course it will use a little bit of energy. So the BMS probably does it only if the SOC is above some value.
3) To try to clarify that, I was wondering if the balancing activity is reported in the logs. But it does not appear clearly in my logs.
4) The string "SOC adjusted for voltage" in the logs seems to be related with some activity of the BMS, probably updating the SOC from different algorithms, and I was wondering if it was balancing the cells at the same time
So, it seems that the way the BMS acts to balance the cells will keep some mysteries (for me at least).
Anyway, probably it does not matter a lot, since I tried to never full charge since many cycles (stopping the charge between 75 and 85% SOC), and the cell balance keeps fine at any time (4 mV).
I will now focus on building my fast charger, as stated elsewhere in this forum, and forget about self balancing that seems to work magically for me