[compiler-rt] Fix issue with compiler-rt tests mixing <atomic> and <stdatomic.h>

Since D97044, libc++ implements <stdatomic.h>, which is not compatible
with the <atomic> header in C++03 mode. To fix the tests, avoid using
<stdatomic.h> at all, since it is not strictly required.

rdar://92867529

Differential Revision: https://reviews.llvm.org/D125118