The backup deadline callback raised _AUTH_DB_LOCKED on ANY backup that had
not finished by the deadline, so a large auth DB on a slow disk that was
still copying pages got the "a running browser holds a write lock" wording,
and the all-locked message told the user to quit the browser for a cause
that was not a lock. Track `remaining` between progress callbacks: a held
write lock fails every step with `remaining` unchanged, while real progress
shrinks it. Only the former keeps the lock wording; the latter reports a
plain "backup exceeded Ns" reason that falls to the details branch.
Review follow-up on #113080.
713a9377cc