feat: 添加 NestJS API 基础设施

apps/api/src/health/health.controller.ts

@@ -0,0 +1,19 @@
+import { Controller, Get, Inject } from "@nestjs/common";
+import { HealthService } from "./health.service.js";
+
+@Controller("health")
+export class HealthController {
+  constructor(
+    @Inject(HealthService) private readonly healthService: HealthService,
+  ) {}
+
+  @Get()
+  check(): Promise<{ status: "ok"; postgres: "up"; redis: "up" }> {
+    return this.healthService.check();
+  }
+
+  @Get("live")
+  live(): { status: "ok" } {
+    return { status: "ok" };
+  }
+}