Previously the restore check only ran lazily on a player's next
message, so files could stay wrongly-removed for an arbitrary amount
of time after the window expired. The frontend now schedules a
setTimeout (using the server-provided deadline, mirroring the terminal
lock's reveal timer) that pings the backend right at the deadline so
the check runs promptly regardless of player activity. Restored via
data-files-removal-deadline on page load too, so a refresh mid-window
doesn't lose the timer.