It’s really hard to understand what you are asking. Might try writing in your native language and having AI translate it?
It kind of looks like you made a lithophane and are wanting to make that into a lightbox?
Vectorization = slicing?
If that is a lithophane, you might change your design to make the lithophane printable alone and then mounts in your lightbox. If possible it can save plastic from bad prints. The way it’s depicted in Studio it looks like there will be lots of support needed and any problems printing the lithophane wastes the box and all that support. Plus the support will possibly be difficult to remove from the back side of the lithophane.