The solution is to install the libclang-rt-22-dev package, which was somehow not installed even though it was recommended by the libclang-common-22-dev package. It provides the /usr/lib/llvm-22/lib/clang/22/lib/linux/libclang_rt.asan-x86_64.a file, which can be seen with apt-file show libclang-rt-22-dev.