fix: project finished backup jobs onto host row + smoke path tweaks

The dashboard's 'Last backup' column reads hosts.last_backup_at /
last_backup_status, but the WS handler only updated hosts.repo_status
on job.finished — backup terminations were silently dropped. Add a
SetHostLastBackup store method and call it from the same job.finished
switch that already handles init jobs.

Also: CLAUDE.md restage block uses /tmp/rm-smoke (the original
default) but the actual dev env runs out of $HOME/smoke. Update the
paths in the doc to match.

internal/store/hosts.go

@@ -81,6 +81,19 @@ func (s *Store) SetHostRepoStatus(ctx context.Context, hostID, status, errMsg st
 	return nil
 }
 
+// SetHostLastBackup projects a finished backup job onto the host row
+// so the dashboard can show last-run state without trawling the jobs
+// table. Called from the WS handler on job.finished where kind=backup.
+func (s *Store) SetHostLastBackup(ctx context.Context, hostID, status string, when time.Time) error {
+	_, err := s.db.ExecContext(ctx,
+		`UPDATE hosts SET last_backup_at = ?, last_backup_status = ? WHERE id = ?`,
+		when.UTC().Format(time.RFC3339Nano), status, hostID)
+	if err != nil {
+		return fmt.Errorf("store: set host last backup: %w", err)
+	}
+	return nil
+}
+
 // DeleteHost removes a host row by id. Returns ErrNotFound if no row
 // matched. Foreign-key cascades (declared on every dependent table —
 // schedules, jobs, snapshots, source_groups, host_credentials, etc.)