where in Airbus FCOM does it say these days that in vicinity of CB's + in cloud the E-AI should remain on even if SAT is less than -40 deg C?
I don't think it does. However this Airbus document "Getting to grips with cold weather operations"
https://skybrary.aero/bookshelf/books/3404.pdf, on page 40 says:
"The engine ice protection system (Nacelle Anti-Ice: NAI) must be immediately activated when encountering the above-noted icing condition. This procedure prevents any ice accretion (anti-icing) on the air intakes of the engines, thus protecting the fan blades from damage due to ingested ice plates (FOD).
When the Static Air Temperature (SAT) is below -40°C the NAI must only be ‘ON’ when the aircraft enters cumulonimbus clouds, or when the Advisory Ice Detection System - if installed - annunciates ICE DETECTED (refer to section A3.3)."
(my bolding)