Since there’s currently (as of July 2019) no Perspective / Distort / Warp tool in Affinity Designer ($49.99) (which I was totally used to for forever in Adobe Illustrator), ya gotta use Affinity Photo ($49.99). And you can open Affinity Photo directly from within Affinity Designer: File > Edit in Photo…
Currently you can only work non-destructively when performing perspective distortions using the Live Perspective Filter (menu Layer ▸ New Live Filter Layer ▸ Distort ▸ Perspective). There’s no similar live filter for warp distortions at the moment.Source: Affinity Forum
(NOTE: when the Perspective pop-up window appears you gotta keep it open while adjusting the Perspective Mesh overlay, otherwise the Mesh overlay vanishes).
The above instructions from Affinity Staff Moderator MEB totally worked for my needs: design vector art in Designer, then open Photo from within Designer and non-destructively distort the perspective of the art.
WARNING: Be aware that the resulting distorted art does NOT remain in vector form. It gets turned into a non-editable bitmap with no vector node points! You can still see the outlines of the art in Outlines Mode in Designer, but you can no longer edit it with the Node Tool once it’s been distorted in Photo.