The SVG's will not help much except when importing into Gimp at a specific size.
Truthfully the book template is very flat anyway except for the gutter (the center between pages)
If the logo crosses the gutter then apply a displacement map see:
https://docs.gimp.org/2.10/en/gimp-filter-displace.html Filters -> Map -> Displace
Not much to say about this except make your logo layer the same size as the map layer (the book demo) otherwise it displaces in the wrong place.
For the rest of the book, make sure any shading covers the logo. Your SVG book demo is not going to much help here, you really need the shading on its own layer.