OK, for a real feature this is not the method to achieve it.
You will need a curve image or better a sketch (DXF,DWG) to place onto the face of YOur part and then You can use this for a normal cutout.
But I think, this will not be a matter of a one shot feature.
Suppose there are several steps necessary to get the result as You want it.
Good evening @And_M_One
The only way I was able to create a single contiguous or seamless surface was by wrapping a sketch, a rectangle, over the surface of a rounded box, creating derived curves and a bounded surface, then applying a textured face style to it.
Ignoring the seam which was some miscalculation, is this what you are looking for when you say
"image project on the whole surface this image filling all the faces"
And no; a bump map texture cannot be used to create a deformation on a Solid Edge body.
This falls in the realms of modeling programs like 3D Studio Max where it is a single-click operation using displacement maps.
<EDIT> Another simple method to create a single surface would be to create a BlueSurf between the top and bottom faces of the block. This will also not leave any seam as seen in the image above.
The face style applied will also stretch over the entire surface without getting split at the edges.
You can use "wrap sketch" to wrap a sketch over multiple surfaces, however, you can't wrap on the whole surfaces in one shot.
P.S.: In italian language it is called "Sagoma schizzo"
Then you can use the "normal cutout" to engrave the surface
In italian it is called "Scavo normale"