fix(gateway): crash safety on screen-share input timeout + proper error serialization

Root cause of "langsung left": YouTube bot-block/403 on u_c1tRmj7E4 (live
stream, LOGIN_REQUIRED) made yt-dlp timeout in resolveInputWithRetry (12s).
The timeout handler did cleanup() (removing once() listeners) THEN
tee.destroy(new Error(...)) — the PassThrough emitted 'error' with NO
listener left → unhandled stream 'error' event → uncaughtException →
gracefulShutdown → bot left voice.

Fix:
- resolveInputWithRetry: tee.destroy() silently after cleanup (error carried
  in the rejection only); add permanent no-op tee.on('error') safety.
- prepareStream: output.on('error') no-op so ffmpeg spawn failure before
  playStream attaches a demux listener never crashes the gateway.
- bootstrap: serialize uncaughtException/ClientError/DB errors with
  {err, errorMsg, stack} (pino only serializes the 'err' magic key — the old
  {error: err} key printed {} so crashes were invisible).

services/discord-gateway/src/app/bootstrap.ts

@@ -222,7 +222,10 @@ export async function initializeDiscordGateway() {
     await initializeDatabase();
     logger.info("PostgreSQL database initialized");
   } catch (err) {
-    logger.error({ error: err }, "Failed to initialize database");
+    logger.error(
+      { err, errorMsg: err instanceof Error ? err.message : String(err) },
+      "Failed to initialize database",
+    );
     throw new DatabaseError(
       `Database initialization failed: ${err instanceof Error ? err.message : String(err)}`,
     );
@@ -267,7 +270,10 @@ export async function initializeDiscordGateway() {
   });
 
   client.on("error", (err) => {
-    logger.error({ error: err }, "Client error");
+    logger.error(
+      { err, errorMsg: err instanceof Error ? err.message : String(err) },
+      "Client error",
+    );
   });
 
   process.on("SIGINT", () => {
@@ -298,7 +304,14 @@ export async function initializeDiscordGateway() {
       );
       return;
     }
-    logger.error({ error: err }, "Uncaught exception");
+    logger.error(
+      {
+        err,
+        errorMsg: err instanceof Error ? err.message : String(err),
+        stack: err?.stack,
+      },
+      "Uncaught exception",
+    );
     gracefulShutdown("uncaughtException");
   });