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(-)

packages/shared/src/logger/index.ts

@@ -17,6 +17,11 @@ const rootLogger = pino({
 
 export type Logger = ReturnType<typeof createChildLogger>;
 
+/**
+ * Alias for backwards compatibility (discord-gateway uses this name).
+ */
+export type CustomLogger = Logger;
+
 /**
  * Returns a child logger bound to the root singleton via pino's .child().
  * Preserves parent context and is efficient (no transport re-init per call).