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At KiCon 2019 there was a presentation on SKiDL which allows you to describe circuits in Python. You can then output a netlist for use in KiCAD's PCB tool (or potentially other EDA tools). I have not tried to use it personally.

https://www.youtube.com/watch?v=WErQYI2A36M

https://github.com/xesscorp/skidl

Yes gEDA is what you want! Each component of gEDA (schematic, layout, etc) works on text files which you can script up easily.

I've heard of people generating designs via scripts in gEDA.

http://www.geda-project.org/