feat(api): 搭建 API 与 Worker 骨架及契约基线

NestJS 11 + Fastify 统一错误体与 trace_id，/health 真实探活 DB/Redis，OpenAPI 3.1 契约含 20 个错误码；shared 包提供错误码、权限点、ULID、分页与通用 schema；worker 完成队列进程骨架。

apps/api/src/common/errors/app-exception.ts

@@ -0,0 +1,25 @@
+import { ERROR_MESSAGES, type ErrorCode, httpStatusOf } from '@lingxi/shared';
+
+export interface AppExceptionOptions {
+  code: ErrorCode;
+  message?: string;
+  details?: unknown;
+}
+
+/**
+ * 业务异常：由统一异常过滤器序列化为 { code, message, details, trace_id }。
+ * 业务代码禁止直接 throw new Error 表达可预期错误。
+ */
+export class AppException extends Error {
+  readonly code: ErrorCode;
+  readonly status: number;
+  readonly details?: unknown;
+
+  constructor(options: AppExceptionOptions) {
+    super(options.message ?? ERROR_MESSAGES[options.code]);
+    this.name = 'AppException';
+    this.code = options.code;
+    this.status = httpStatusOf(options.code);
+    this.details = options.details;
+  }
+}