I think all those links mention コート somewhere, can we really say that 道行き on its own means a type of coat? Most of those links call it a 道行コート, maybe that should be the word?
I\ve always just called it a 道行き. So, I checked with people I know in Kyoto that regularly wear kimono and checked in with a multilingual group that studies and wears wafuku, and both groups some also checked various Japanese dictionaries. And the answers were mixed. When speaking they reported that sometimes they called it a michiyuki but that it really was a michiyuki ko-to. Some dictionaries include as a definition under michiyuki -- added the ko-to to the word, and others gave it it's own entry as michiyuki ko-to. So, nothing seems right or wrong as long as you can find it when you enter michiyuki or 道行(き) when you go to look it up.
A type of light-weight coat worn over a kimono for protection from rain, splashes. Usually with a squared front neck opening.
See the following link for images from Google.
https://www.google.com/search?q=%E9%81%93%E8%A1%8C%E3%81%8D&newwindow=1&sxsrf=ALiCzsanHJPUB4lttYft8nVGU6SodN6Ffg:1658564899902&source=lnms&tbm=isch&sa=X&ved=2ahUKEwio8sfdy475AhWfQ_EDHUiFDg0Q_AUoAXoECAEQAw&biw=1104&bih=584&dpr=3