add NestJS skeleton and GET /api/health-check.

Thin API bootstrap with config module and nullcart-style health route for Docker checks.

backend/src/AppModule.ts

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+import { Module } from '@nestjs/common';
+import { ConfigModule } from '@nestjs/config';
+import appConfig from './config';
+import { HealthCheckModule } from './modules/healthCheck/HealthCheckModule';
+
+@Module({
+    imports: [
+        ConfigModule.forRoot({
+            isGlobal: true,
+            load: [appConfig]
+        }),
+        HealthCheckModule
+    ]
+})
+export class AppModule {}

backend/src/config/index.ts

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+import { registerAs } from '@nestjs/config';
+import { AppConfig } from '../types/AppConfig';
+import { NodeEnv } from '../types/NodeEnv';
+
+const env = (key: string): string => process.env[key] || '';
+
+const envInt = (key: string): number => parseInt(env(key), 10);
+
+export const getAppConfig = (): AppConfig => {
+    const rawOrigins = env('CORS_ORIGINS');
+
+    return {
+        port: envInt('BACKEND_PORT'),
+        nodeEnv: env('NODE_ENV') as NodeEnv,
+        corsOrigins: rawOrigins
+            .split(',')
+            .map(o => o.trim())
+            .filter(Boolean)
+    };
+};
+
+export default registerAs('app', getAppConfig);

backend/src/main.ts

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+import { ValidationPipe } from '@nestjs/common';
+import { ConfigService } from '@nestjs/config';
+import { NestFactory } from '@nestjs/core';
+import { AppModule } from './AppModule';
+import { AppConfig } from './types/AppConfig';
+
+async function bootstrap() {
+    const app = await NestFactory.create(AppModule);
+
+    const configService = app.get(ConfigService);
+    const { port, corsOrigins } = configService.get('app') as AppConfig;
+
+    app.setGlobalPrefix('api');
+
+    app.useGlobalPipes(
+        new ValidationPipe({
+            transform: true,
+            transformOptions: { enableImplicitConversion: true }
+        })
+    );
+
+    app.enableCors({
+        origin: corsOrigins,
+        credentials: true
+    });
+
+    await app.listen(port);
+}
+
+void bootstrap();

backend/src/modules/healthCheck/HealthCheckModule.ts

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+import { Module } from '@nestjs/common';
+import { HealthCheckController } from './controllers/HealthCheckController';
+
+@Module({
+    controllers: [HealthCheckController]
+})
+export class HealthCheckModule {}

backend/src/modules/healthCheck/controllers/HealthCheckController.ts

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+import { Controller, Get, HttpStatus, Res } from '@nestjs/common';
+import type { Response } from 'express';
+
+@Controller('/health-check')
+export class HealthCheckController {
+    @Get('/')
+    getStatus(@Res() res: Response) {
+        return res.sendStatus(HttpStatus.OK);
+    }
+}

backend/src/types/AppConfig.ts

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+import { NodeEnv } from './NodeEnv';
+
+export type AppConfig = {
+    port: number;
+    nodeEnv: NodeEnv;
+    corsOrigins: string[];
+};

backend/src/types/NodeEnv.ts

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+export enum NodeEnv {
+    Development = 'development',
+    Production = 'production'
+}