[compiler-rt][builtins] Switch libatomic locks to pthread_mutex_t (#94374)

When an uninstrumented libatomic is used with a TSan instrumented
memcpy, TSan may report a data race in circumstances where writes are
arguably safe.

This occurs because __atomic_compare_exchange won't be instrumented in
an uninstrumented libatomic, so TSan doesn't know that the subsequent
memcpy is race-free.

On the other hand, pthread_mutex_(un)lock will be intercepted by TSan,
meaning an uninstrumented libatomic will not report this false-positive.

pthread_mutexes also may try a number of different strategies to acquire
the lock, which may bound the amount of time a thread has to wait for a
lock during contention.

While pthread_mutex_lock has a larger overhead (due to the function
call and some dispatching), a dispatch to libatomic already predicates
a lack of performance guarantees.