refactor: migrate discord-gateway from winston to @bete/shared/logger and utils

- Replace all local logger imports (../../shared/logger/logger.js) with @bete/shared/logger across 26 files
- Remove winston dependency, add pino to discord-gateway package.json
- Delete shared/logger/logger.ts (winston-based, 132 lines) and serialization.ts (109 lines)
- Replace local retryWithBackoff imports with @bete/shared/utils across 6 files
- Delete shared/utils/retry.ts (42 lines)
- Add CustomLogger type alias to @bete/shared/logger for backwards compatibility
- Remove logger param from all retryWithBackoff calls and uploadToTele interfaces
- Frontend: convert entity type files to re-exports from shared/api/client.ts
- Full monorepo typecheck clean (4/4 packages)

35 files changed, 42 insertions(+), 488 deletions(-)

services/discord-gateway/src/modules/ai-moderation/llmClient.ts

@@ -8,9 +8,9 @@
 
 import OpenAI from "openai";
 import { config } from "../../shared/config/config.js";
-import { retryWithBackoff } from "../../shared/utils/retry.js";
+import { retryWithBackoff } from "@bete/shared/utils";
 import { withLlmConcurrency } from "./concurrencyLimiter.js";
-import { createChildLogger } from "../../shared/logger/logger.js";
+import { createChildLogger } from "@bete/shared/logger";
 
 const log = createChildLogger("llm-client");
 
@@ -136,7 +136,6 @@ export async function llmChat(
       minTimeout: 0,
       maxTimeout: 0,
       factor: 2,
-      logger: log,
     },
   );
 }