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/modules/ai-moderation/ai-analysis-worker.ts

@@ -316,11 +316,13 @@ async function processBatch(job: {
   // The orchestrator handles text/media split + caching + parallel paths
   // internally, so a 20-message batch = 1 text LLM call (+1 media call
   // when media is present), not N per-message calls.
+  const analysisStart = Date.now();
   const moderationResult = await runModerationAnalysis({
     targets: readyMessages,
     contextBlock,
     attachments,
   });
+  const analysisDurationMs = Date.now() - analysisStart;
 
   const results = moderationResult.results.map((r) =>
     normalizeResult(
@@ -342,6 +344,7 @@ async function processBatch(job: {
       confidence: result.confidence,
       recommendedAction: result.recommendedAction,
       analyzedAt: Date.now(),
+      analysisDurationMs,
       error: result.status === "error" ? result.analysis : null,
     },
   }));