In Affinity Designer you can use the Subtract/Intersect/Divide commands, the icons are near the top right of your toolbar at the top of the screen.
Say you trace one shape exactly the way it needs to be, then the adjacent shape is drawn slightly oversized/overlapping, then use those tools to trim away the oversized part.
Perfectly overlapping cuts or scores will result in slightly wider kerf cuts in those areas. It maybe not a big deal for cuts since the pieces will be cut apart anyway, but overlapping scores will be a bit more noticeable. For those, you can break one of the paths into an open shape so it just stops at the point where it intersects the other one.
There is a process in the graphics trade called “Color Trapping” which is basically digging through artwork and removing areas that overlap. In modern digital printing this is not required but it is in press printing or screen printing where overlapping press plates or screens will result in colors that print through/over each other and don’t look good. That has carried over into the vinyl cutting side of things, and machines like vinyl cutters, lasers, CNC etc that rely on tool paths you generally don’t want overlap.