@driver my goodness, why didn't you say so right at the beginning? That threw me completely off-course :D
I've checked now, and it also does not work for me. I have checked on custom-built Qt and also on official release (Qt 6.4.3 in both cases).
So, the documentation here is wrong. Apparently, the solution is not to add private stuff to find_package but instead only link to core library, like so:
target_link_libraries(${PROJECT_LIB}
PUBLIC Qt${QT_VERSION_MAJOR}::Core
PUBLIC Qt${QT_VERSION_MAJOR}::CorePrivate
)