Here's a good Hackaday article on converting SVG to PCB file formats:
PCBModE is one package I tried for a while:
Boldport uses this toolchain to make beautiful PCBs relying heavily on SVG: https://www.boldport.com/
I had a hard time with all these packages, however, and ended up just hacking it together by hand with python code and outputting in KiCAD format. I wasn't even able to get KiCAD to read/render it properly (too many weird elements), but since OSH Park (where I got my PCBs from) takes KiCAD format directly and gives you a preview, that all worked fine, and when I ordered my PCBs, they arrived in working condition just fine the first time.
So yeah, SVG can do a lot, including make funky PCBs.
The easiest way is to design the coil as a part, but you can use traces and arcs and stuff like normal in that.
I think I used OpenSCAD to export to SVG.