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/package.json

@@ -0,0 +1,42 @@
+{
+  "name": "@lingxi/api",
+  "version": "0.1.0",
+  "private": true,
+  "scripts": {
+    "dev": "tsx watch src/main.ts",
+    "build": "tsc -p tsconfig.build.json",
+    "start": "node dist/main.js",
+    "typecheck": "tsc -p tsconfig.json --noEmit",
+    "test": "vitest run --coverage",
+    "test:int": "vitest run --config vitest.int.config.ts"
+  },
+  "dependencies": {
+    "@fastify/cors": "11.3.1",
+    "@fastify/helmet": "13.2.0",
+    "@fastify/static": "10.1.8",
+    "@lingxi/shared": "workspace:*",
+    "@nestjs/common": "11.2.8",
+    "@nestjs/core": "11.2.8",
+    "@nestjs/platform-fastify": "11.2.8",
+    "@nestjs/swagger": "11.4.7",
+    "@prisma/client": "6.19.3",
+    "dotenv": "18.0.9",
+    "fastify": "5.12.7",
+    "ioredis": "5.11.1",
+    "nestjs-pino": "5.3.1",
+    "pino": "10.4.0",
+    "pino-http": "11.0.0",
+    "reflect-metadata": "0.2.2",
+    "rxjs": "7.8.2",
+    "zod": "3.25.76"
+  },
+  "devDependencies": {
+    "@nestjs/testing": "11.2.8",
+    "@types/node": "24.19.2",
+    "@vitest/coverage-v8": "3.2.7",
+    "pino-pretty": "13.2.0",
+    "tsx": "4.23.15",
+    "typescript": "5.9.3",
+    "vitest": "3.2.7"
+  }
+}