I think I've come to understand what has been happening. My pyproject.toml names the project "example". Since my source directory has a folder named "example" with an __init__.py in it, scikit-build has been copying that directory, possibly from install(TARGETS example LIBRARY DESTINATION example)

My fix was to remove the CMakeLists.txt from the "example" directory, and remove add_subdirectory(src/example) from my top-level CMake file.