I select elements in VCarve Pro and export them to DXF instead of SVG. Sketchup is very happy importing DXF files since it is ostensibly a CAD program.
There are some (an understatement) manipulations needed within Sketchup. You have to explode the imported DXF, use a plugin to generate faces, and then extrude the result to the thickness of the actual component. Also, you have to know how to rotate, align, group, color, etc. the components.
It can be a bit tedious - and I don’t do it with every project - but sometimes a full 3D CAD model of what you’re building is invaluable. For the purposes of a relatively complicated build like this spice rack, I felt it was worth the effort.
I’m attaching some screens of my workflow to give you an idea of how I do it.