Thanks a lot for the hint. This worked for me.
I was confused because the following code just works for me without using $<SEMICOLON>.
Both files are compiled in this case.
cmake_minimum_required(VERSION 3.24)
add_library(alice
src/alice.c
"$<$<IN_LIST:${CMAKE_SYSTEM_PROCESSOR},x86;x86_64>:src/conditional_file.c>"
)