feat: Android download page, analysis retry and a collapsible search

- /android is a public page with the latest APK, the server address to copy
  and three install steps; linked from the sign-in screen and the profile menu
- failed audio analysis can be retried from the library page, which also shows
  the most common error; the analyzer no longer burns attempts on files that
  are missing because the disk is not mounted
- the top bar search folds into a round button and slides open on click, "/"
  or Ctrl+K

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

services/api/internal/library/store.go

@@ -605,7 +605,7 @@ func (st *Store) AlbumCoverPath(ctx context.Context, albumID uuid.UUID) (*string
 // AnalysisCounts — состояние очереди аудиоанализа.
 type AnalysisCounts struct {
 	Queued, Running, Done, Failed int
-	AnalyzerVer                   *string
+	AnalyzerVer, TopError         *string
 }
 
 // AnalysisCounts считает задачи анализа по статусам и текущую версию анализатора.
@@ -614,14 +614,27 @@ func (st *Store) AnalysisCounts(ctx context.Context) (AnalysisCounts, error) {
 	err := st.pool.QueryRow(ctx, `
 		SELECT count(*) FILTER (WHERE status = 'queued'), count(*) FILTER (WHERE status = 'running'),
 			count(*) FILTER (WHERE status = 'done'), count(*) FILTER (WHERE status = 'failed'),
-			(SELECT analyzer_ver FROM track_features ORDER BY analyzed_at DESC LIMIT 1)
-		FROM analysis_jobs`).Scan(&c.Queued, &c.Running, &c.Done, &c.Failed, &c.AnalyzerVer)
+			(SELECT analyzer_ver FROM track_features ORDER BY analyzed_at DESC LIMIT 1),
+			(SELECT error FROM analysis_jobs WHERE status = 'failed' AND error IS NOT NULL
+			 GROUP BY error ORDER BY count(*) DESC LIMIT 1)
+		FROM analysis_jobs`).Scan(&c.Queued, &c.Running, &c.Done, &c.Failed, &c.AnalyzerVer, &c.TopError)
 	if err != nil {
 		return AnalysisCounts{}, fmt.Errorf("library: analysis counts: %w", err)
 	}
 	return c, nil
 }
 
+// RetryFailedAnalysis возвращает неудавшиеся задачи анализа в очередь с нуля попыток.
+func (st *Store) RetryFailedAnalysis(ctx context.Context) (int, error) {
+	tag, err := st.pool.Exec(ctx, `
+		UPDATE analysis_jobs SET status = 'queued', attempts = 0, error = NULL, updated_at = now()
+		WHERE status = 'failed'`)
+	if err != nil {
+		return 0, fmt.Errorf("library: retry analysis: %w", err)
+	}
+	return int(tag.RowsAffected()), nil
+}
+
 // WaveMetrics — метрики волны за 7 дней (docs/recommendations.md#1-цели-и-как-измеряем-успех).
 type WaveMetrics struct {
 	Served, Sessions int