Cold Brew is an extraction method which takes place at ambient or cold temperature and without pressure. The pump on the La Specialista runs with a dedicated program which extracts coffee withouht producing pressure, this is why the pressure gauge should not move.
If during Cold Brew extraction the pressure gauge climbs up then you can try to make the grind size coarser.
If your coffee is too fresh (roasted <10 days before) it might need a few additional days to degas and not produce pressure during Cold Brew extractions.