I was reading the war plugin's overlay documentation and it said:
targetPath - the target relative path in the webapp structure, which is only available for overlays of type war. By default, the content of the overlay is added in the root structure of the webapp.
But I'm trying to overlay a jar, not a war. I don't want the files to be at the root directory.
Answering my own question:
Turns out that documentation is wrong and you can use a targetPath with a type,
jar
.