refactor: atomic, DRY, and logging improvements across codebase

- Split llmModerationClient.ts (2170 lines) into 5 focused sub-modules
- Split aiAnalyzer.ts (1282 lines) into 4 modular pipelines
- Split messages.db.ts (826 lines) into 5 domain-specific modules
- Moved shared schema to @bete/shared, eliminated backend duplication
- Added createChildLogger to all voice-recording and AI moderation modules
- Extracted tryCommandThenFallback, normalizeMediaState, DEFAULT_VOICE_STATUS
- Created shared pagination.ts utility, eliminated 5+ cursor-pagination duplications
- Created shared messageMapper.ts for row mapping
- Standardized backend error handling with asyncHandler
- Added frontend createLogger utility and useAsyncAction hook
- Added structured logging to frontend hooks, socket, and API client

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

services/discord-gateway/src/modules/message-capture/pagination.ts

@@ -1,21 +1,36 @@
+import { createChildLogger } from "@bete/shared/logger";
+
+const logger = createChildLogger("pagination");
+
 export interface CursorData {
   created_at: number;
   id: string;
 }
 
 export function encodeCursor(data: CursorData): string {
-  return Buffer.from(JSON.stringify(data)).toString("base64");
+  const encoded = Buffer.from(JSON.stringify(data)).toString("base64");
+  logger.debug({ id: data.id, createdAt: data.created_at }, "Encoded cursor");
+  return encoded;
 }
 
 export function decodeCursor(cursor?: string): CursorData | null {
-  if (!cursor) return null;
+  if (!cursor) {
+    logger.debug("No cursor provided to decode");
+    return null;
+  }
   try {
     const data = JSON.parse(Buffer.from(cursor, "base64").toString("utf-8"));
     if (typeof data.created_at === "number" && typeof data.id === "string") {
+      logger.debug(
+        { id: data.id, createdAt: data.created_at },
+        "Decoded cursor",
+      );
       return data;
     }
+    logger.warn({ cursor }, "Decoded cursor has invalid shape");
     return null;
-  } catch {
+  } catch (err) {
+    logger.warn({ cursor, error: String(err) }, "Failed to decode cursor");
     return null;
   }
 }