feat: add HealthController with database connection check

Introduced a HealthController to verify application status. Includes an endpoint to check database connectivity and returns health status with a timestamp.

backend/src/health.controller.ts

@@ -0,0 +1,28 @@
+import { Controller, Get } from "@nestjs/common";
+import { sql } from "drizzle-orm";
+import { DatabaseService } from "./database/database.service";
+
+@Controller("health")
+export class HealthController {
+	constructor(private readonly databaseService: DatabaseService) {}
+
+	@Get()
+	async check() {
+		try {
+			// Check database connection
+			await this.databaseService.db.execute(sql`SELECT 1`);
+			return {
+				status: "ok",
+				database: "connected",
+				timestamp: new Date().toISOString(),
+			};
+		} catch (error) {
+			return {
+				status: "error",
+				database: "disconnected",
+				message: error.message,
+				timestamp: new Date().toISOString(),
+			};
+		}
+	}
+}