The goal was to distort the perspective of vector art in Affinity Designer. Unfortunately, the Distort Perspective tool is only available in Affinity Photo (which transforms the original vector art into raster art). This is not ideal. I wanted to distort the perspective of vector art like I could in Adobe Illustrator, not end up with raster art.
For now, this is the only way to distort the perspective of vector art in Affinity Designer: by opening Affinity Photo directly from within Affinity Designer: File > Edit in Photo. Which produces a raster art result.
Currently you can only work non-destructively when performing perspective distortions using the Live Perspective Filter (menu Layer ▸ New Live Filter Layer ▸ Distort ▸ Perspective).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, as it started out. It gets turned into a non-node-points non-editable bitmap! 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.