Also note, the Parallel constraint was the easiest to show the problem, it does it with all constraints.
The 3rd image shows a comparison of constrained lines on the right, to directed lines on the left, showing that it's not typical staircase or anti alias. I've attached some images to show the error. However, with Affinity Designer the lines are a little wobbly, though they are parallel and Lazy Nezumi connects to Designer fine. If I use the parallel lines option with Affinity Photo, lines (Paint Brush tool) drawn are nice and straight, parallel lines as expected. Once connected it allows you to constrain to things like perspective or parallel lines etc. It automatically hooks into PS but you can manually hook any graphics app by hovering in the app. I use a Wacom Cintiq tablet and the helper tool, Lazy Nezumi Pro, that basically constrains the cursor in any connected program. The issue points to a problem in Designer as it works absolutely fine in Photo. I'm relatively new to the Affinity suite but generally getting on OK, though I've come across an issue with one of the helper tools I use.