feat: surface AI analysis duration across gateway, backend, and FE

Adds per-message AI moderation analysis time (ai_analysis_duration_ms)
so operators can see how long the LLM took to moderate each message.

Gateway:
- messagesTable: new ai_analysis_duration_ms (bigint) column.
- AIAnalysisUpdate + buildAIAnalysisSet: carry analysisDurationMs through
  both single and bulk update paths.
- ai-analysis-worker: measure wall-clock time around runModerationAnalysis
  and attach it to every result in the batch.

Backend:
- Mirror schema column; messageMapper maps ai_analysis_duration_ms;
  moderation-types + MappedMessage expose it.

Frontend:
- message.ts type gains ai_analysis_duration_ms.
- AiBadge (messages view) shows 'status · 1.2s' when duration is present;
  analysis view badge mirrors the same formatting.

DB:
- scripts/add-ai-analysis-duration.sql (idempotent ADD COLUMN IF NOT EXISTS).

No behavior change for moderation logic; null until new gateway build
records values.

services/frontend/src/lib/types/message.ts

@@ -130,6 +130,7 @@ export interface MessageRecord {
   ai_recommended_action?: AiRecommendedAction | null;
   ai_error?: string | null;
   ai_analyzed_at?: number | null;
+  ai_analysis_duration_ms?: number | null;
   /** Detail-only: number of past edits (message_edits snapshots) */
   edit_count?: number;
   /** Detail-only: previous content snapshots, newest first */