There are several different possible ways for doing this as vectors! - Though the quickest would probably be to use vector shapes and apply some FX effect filters to those (3D, outer shadow, etc.) ...
card_stack.afdesign
But the bad here in terms of vectors is, that the Affinity FX effects will be rasterized on export and thus be stored as bitmap representations inside a vector file! - A better way would be to do it all in plain vectors then, namely also the 3D look and also the shadows etc. For a more real 3D look the isometric design features of Designer can be helpful to use, for the shadows then either some vector gradient or a bunch of combined vector lines/shapes which resemble a shadow.
So the above shown is only a quick'n'dirty 5 minute sample of how to do it the very fast way with Designer!