You can extract the face with the holes inside it using explode, then picking the face, and then use OffsetSrf to offset by 0.7 mm, making sure Solid = No.
Then This will reproduce your surface offset.
You can then just delete all of the side (little) faces (making use of explode again if needed, on your “Cartier” face.
You then directly loft all of the sides back together. I would suggest the holes can be easily remade, as at the moment the cutouts on your cylinders are all uneven, and make no sense.
From your file, the cylindrical cutouts are a little confused, and I cannot tell if they are supposed to contain interior cylinders for mounting gems, or if the cylinders are just wrongly sized.