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/server/ws/handler.go

@@ -227,11 +227,17 @@ func dispatchAgentMessage(ctx context.Context, c *Conn, hostID string, env api.E
 		// a *success* — restic's idempotent init returns that when the
 		// repo is already initialised, which is the happy path for
 		// onboarding against an existing repo.
-		if job, err := deps.Store.GetJob(ctx, p.JobID); err == nil && job != nil &&
-			job.Kind == string(api.JobInit) {
-			status, errOut := repoStatusFromInit(string(p.Status), errMsg)
-			if err := deps.Store.SetHostRepoStatus(ctx, hostID, status, errOut); err != nil {
-				slog.Warn("ws: set host repo status", "host_id", hostID, "err", err)
+		if job, err := deps.Store.GetJob(ctx, p.JobID); err == nil && job != nil {
+			switch job.Kind {
+			case string(api.JobInit):
+				status, errOut := repoStatusFromInit(string(p.Status), errMsg)
+				if err := deps.Store.SetHostRepoStatus(ctx, hostID, status, errOut); err != nil {
+					slog.Warn("ws: set host repo status", "host_id", hostID, "err", err)
+				}
+			case string(api.JobBackup):
+				if err := deps.Store.SetHostLastBackup(ctx, hostID, string(p.Status), p.FinishedAt); err != nil {
+					slog.Warn("ws: set host last backup", "host_id", hostID, "err", err)
+				}
 			}
 		}
 		if deps.JobHub != nil {

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.)