The multi-op live status heartbeated every 15 s, so an operator who left the
log open but stopped working still showed on air. Now it publishes an explicit
online flag: online when a new contact was logged within the last 5 minutes,
offline otherwise. live_status gains `online` + `last_qso_at` columns (added to
existing tables via ALTER). Logging a QSO (manual, UDP, ADIF monitor) stamps the
time and republishes at once, so they flip back online instantly.
At launch the last-QSO time is seeded from the DB (Repo.LastQSOTime), so an
operator who worked someone just before starting OpsLog is shown online right
away rather than offline until their next contact. LiveLastQSOAgeSec exposes it
to the UI badge.