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.

scripts/add-ai-analysis-duration.sql

@@ -0,0 +1,10 @@
+-- Migration: add ai_analysis_duration_ms to messages
+-- Tracks how long the AI moderation LLM call took, per message (ms).
+-- Idempotent: safe to re-run.
+--
+-- Run against the production GMW database, e.g.:
+--   PGPASSWORD=*** psql -h 100.121.180.82 -p 6432 -U asephs -d dcbot \
+--     -f scripts/add-ai-analysis-duration.sql
+
+ALTER TABLE "messages"
+  ADD COLUMN IF NOT EXISTS "ai_analysis_duration_ms" BIGINT;