Thanks for the example!
Irrlicht3d and VulkanSceneGraph are fundamentally different under the hood. 3D objects in VSG must be given as indexed face sets with proper shading setup. Size, orientation and position must be set by a transformation matrix. For a couple of primitive objects (box, shere, cone,...) we have convenience functions. User defined objects can be loaded via 3d-graphic files. We recommend the wavefront file format (*.obj/*.mtl) because it is human readable and has an easy structure.
demo_VSG_assets shows 3D objects bound to bodies and scenery objects, which are meant for decoration (treas, houses, animals,...). The scenery objects can also be moved, oriented and sized. In the demo you have the (Utah)teapot, the (Stanford)bunny, the teleporting sphere and of course the forklift truck. You could try at first this basic approach.
It should give you a similar result you have in the Irrlicht based demo. The sizing of an object only by a transformation matrix is of course limited and does not consider shape changes of the object during expansion/compression it is just linear mathematical sizing. There is a more sophisticated solution with vertex/normal/color updates but this is tricky and should not be tried as a first approach.
Good luck!