feat(web): honest, state-aware summarize status with charm spinner (ADR-025)

Clicking Summarize polled /status, which knew only "spinning" or "done". The web
ProcessVideo recorded an outcome only on success, so a 429'd or caption-less
click left transcript_status unset and the poll silently reverted to the
Summarize button — the rate limit was invisible and the click felt broken.

- ProcessVideo now records rate_limited / none / fetched (mirrors the runner); a
  rate-limited video keeps its requested flag so the background sweep retries it.
- /status is state-aware: summary card (done), working spinner (in-flight),
  a calm "waiting on rate limit, will retry" card that keeps polling so the
  summary lands on its own (no re-click), and a terminal "no captions" card.
- Charm status text (Claude-Code / Crush inspired): the spinner cycles playful
  tapir-themed gerunds via CSS only (no JS), decorative + an sr-only stable
  status line for a11y.

Pillar A (foreground fetch priority lane) is a separate follow-up.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

cmd/tapir/processor.go

@@ -132,7 +132,28 @@ func (p *engineProcessor) ProcessVideo(ctx context.Context, userID, videoID stri
 	if err != nil {
 		return fmt.Errorf("process video %q: %w", videoID, err)
 	}
-	if res.Summary != nil {
+
+	// Record the outcome so the status endpoint can show honest state (ADR-025):
+	// a 429'd or caption-less click used to leave transcript_status unset, so the
+	// poll silently reverted to the "Summarize" button. Mirror the runner: stamp
+	// rate_limited / none / fetched. A rate-limited video keeps its requested flag
+	// so the background sweep retries it; none and fetched are terminal here.
+	switch {
+	case res.Skipped && res.TranscriptSource == string(domain.SourceRateLimited):
+		if err := p.store.SetTranscriptStatus(ctx, userID, videoID, "rate_limited"); err != nil {
+			return fmt.Errorf("set rate_limited status %q: %w", videoID, err)
+		}
+	case res.Skipped:
+		if err := p.store.SetTranscriptStatus(ctx, userID, videoID, "none"); err != nil {
+			return fmt.Errorf("set none status %q: %w", videoID, err)
+		}
+		if err := p.store.ClearSummarizeRequested(ctx, userID, videoID); err != nil {
+			return fmt.Errorf("clear summarize flag %q: %w", videoID, err)
+		}
+	case res.Summary != nil:
+		if err := p.store.SetTranscriptStatus(ctx, userID, videoID, "fetched"); err != nil {
+			return fmt.Errorf("set fetched status %q: %w", videoID, err)
+		}
 		if err := p.store.ClearSummarizeRequested(ctx, userID, videoID); err != nil {
 			return fmt.Errorf("clear summarize flag %q: %w", videoID, err)
 		}