refactor: break monorepo into 3 standalone services (gateway, backend, frontend)

- Remove pnpm workspace, moon repo, and all monorepo tooling
- Delete packages/shared/, embed shared code directly into each service
- Copy packages/shared/src/* -> services/backend/src/shared/ and services/discord-gateway/src/shared/
- Replace all @bete/shared imports with @/shared/ path alias
- Remove @bete/shared workspace dependency from both services
- Update root package.json scripts from --filter to --prefix
- Rewrite Dockerfiles to build each service standalone
- Clean up biome.json, .gitignore, remove root drizzle.config.ts

services/backend/src/shared/logger/index.ts

@@ -0,0 +1,31 @@
+import pino from "pino";
+
+const rootLogger = pino({
+  level: process.env.LOG_LEVEL || "info",
+  transport:
+    process.env.NODE_ENV === "development"
+      ? {
+          target: "pino-pretty",
+          options: {
+            colorize: true,
+            translateTime: "SYS:standard",
+            ignore: "pid,hostname",
+          },
+        }
+      : undefined,
+} as pino.LoggerOptions);
+
+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).
+ */
+export function createChildLogger(context: string) {
+  return rootLogger.child({ context });
+}