[Sanitizer] Modify test to avoid bot timeouts

Change the mutex type to one that initializes on construction and
hopefully avoid what appear to be deadlock failures in the new test
on a couple bots, e.g.:

https://green.lab.llvm.org/green/job/clang-stage1-RA/24140/testReport/SanitizerCommon-Unit/__Sanitizer-x86_64-Test/SanitizerCommon_ReportFile/