Fritzing has a difficult part making process, because you have to make 3 drawings, but that’s what you pay for with the convenience of 3 simultaneous linked views, ie pain at the start but convenience latter. KiCad is a pain because it’s separate programs in one wrapper that aren’t connected.
Whenever you do a drawing or modify a drawing always add a 0.100" grid with snap to centre and you can’t go wrong. For Inkscape File/Document Properties/Grid.
I put a 20 pin header on the PCB drawing and it’s 20 pins outside to outside. The old Breadboard svg connected, but when I zoomed in on the connectors the right-hand ones were centre locked and the left ones were West locked - you can see it in your top pic -, so to make it neat I made it 21 pins so the vertical pins line up. Is the part supposed to mate with a 20 pin part in Breadboard.
I’m sure you guys will sort it out now you know about the 0.100" grid.