Thank you everyone for your answers, I wasn’t receiving any email telling me you had answered, so sorry for my late response.
The shunt was apparently the culprit.
I had a guy from Azimut Electronics (the company who sold the shunt, Victron and batteries) checked the batteries: he got a correct reading. So then we changed the shunt…to see what happened. The new shunt was picking the 100% charge of batteries, we turned on a light and it was showing the discharging amperage. I turned it off: the amperage = 0…and right then we connected the old shunt again…and it was picking the discharging amperage when the light wasn’t turned on anymore, so we deducted it was the shunt. I got it replaced.
Now there’s nothing that seems odd in its readings…the batteries are so fully charged that solar panels nor driving charges them, I guess because of the BMS (I have to say the lithium batteries have been such a qualitative leap from AGM…sometimes I can’t even believe this).
I have a trip ahead so it’ll be the right moment to turn stuff on, and see if batteries get recharged while driving or solar powered (if sunny) and see if the new shunt shows correct and coherent readings.
Muchas GRACIAS, you’re a great community!
Greetings from some rural area in Spain.