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/discord-gateway/src/shared/database/schema.ts

@@ -62,6 +62,9 @@ export const pgMessagesTable = pgTable(
       enum: ["none", "monitor", "warn", "review", "delete", "escalate"],
     }),
     ai_analyzed_at: pgBigint("ai_analyzed_at", { mode: "number" }),
+    ai_analysis_duration_ms: pgBigint("ai_analysis_duration_ms", {
+      mode: "number",
+    }),
     ai_error: pgText("ai_error"),
   },
   (table) => ({