fix: Health check Redis 상태를 실제 PING 체크로 변경 (#156)

- not_configured 하드코딩 제거
- RedisConnection 주입 후 PingAsync()로 실제 연결 상태 확인
- 응답에 latency 포함

Closes #156

SPMS.API/Controllers/PublicController.cs

@@ -4,6 +4,7 @@ using Microsoft.EntityFrameworkCore;
 using Swashbuckle.AspNetCore.Annotations;
 using SPMS.Domain.Common;
 using SPMS.Infrastructure;
+using SPMS.Infrastructure.Caching;
 using SPMS.Infrastructure.Messaging;
 
 namespace SPMS.API.Controllers;
@@ -15,15 +16,18 @@ namespace SPMS.API.Controllers;
 public class PublicController : ControllerBase
 {
     private readonly AppDbContext _dbContext;
+    private readonly RedisConnection _redisConnection;
     private readonly RabbitMQConnection _rabbitConnection;
     private readonly RabbitMQInitializer _rabbitInitializer;
 
     public PublicController(
         AppDbContext dbContext,
+        RedisConnection redisConnection,
         RabbitMQConnection rabbitConnection,
         RabbitMQInitializer rabbitInitializer)
     {
         _dbContext = dbContext;
+        _redisConnection = redisConnection;
         _rabbitConnection = rabbitConnection;
         _rabbitInitializer = rabbitInitializer;
     }
@@ -47,8 +51,18 @@ public class PublicController : ControllerBase
             allHealthy = false;
         }
 
-        // 2. Redis 연결 확인 (Phase 3-2에서 구현 예정)
+        // 2. Redis 연결 확인
-        checks["redis"] = new { status = "not_configured" };
+        try
+        {
+            var db = await _redisConnection.GetDatabaseAsync();
+            var pong = await db.PingAsync();
+            checks["redis"] = new { status = "healthy", latency = $"{pong.TotalMilliseconds:F1}ms" };
+        }
+        catch (Exception ex)
+        {
+            checks["redis"] = new { status = "unhealthy", error = ex.Message };
+            allHealthy = false;
+        }
 
         // 3. RabbitMQ 연결 확인
         var rabbitConnected = _rabbitConnection.IsConnected;