feat: add backend logger matching frontend text format

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

packages/backend/src/index.ts

@@ -13,17 +13,14 @@ import { schema } from "./graphql/index";
 import { buildContext } from "./graphql/context";
 import { db } from "./db/connection";
 import { redis } from "./lib/auth";
+import { logger } from "./lib/logger";
 
 const PORT = parseInt(process.env.PORT || "4000");
 const UPLOAD_DIR = process.env.UPLOAD_DIR || "/data/uploads";
 const CORS_ORIGIN = process.env.CORS_ORIGIN || "http://localhost:3000";
 
 async function main() {
-  const fastify = Fastify({
-    logger: {
-      level: process.env.LOG_LEVEL || "info",
-    },
-  });
+  const fastify = Fastify({ loggerInstance: logger });
 
   await fastify.register(fastifyCookie, {
     secret: process.env.COOKIE_SECRET || "change-me-in-production",