After https://crrev.com/c/2529140, the actual data race should already
be fixed. This CL updates documentation (by moving the field to the
fields protected by {mutex_}), and updates {SetHighPriority} to also
take the mutex. This change is not strictly necessary, because this
method is only called right after creating the object, so no other
threads have access to it yet. But relying on that seems brittle, and
moving the initialization to the constructor is a bigger refactoring
that I don't consider worth it at the moment. The whole priority
management will probably be refactored again soon anyway.

R=ahaas@chromium.org

Bug: v8:11141
Change-Id: I496b619d551aeb584bd6e777c04ed4df076c3ae9
Reviewed-on: https://chromium-review.googlesource.com/c/v8/v8/+/2529143Reviewed-by: Andreas Haas <ahaas@chromium.org>
Commit-Queue: Clemens Backes <clemensb@chromium.org>
Cr-Commit-Position: refs/heads/master@{#71113}