feat: DB DI 전환 + download 하위 호환성 + race condition 수정

- middleware(Auth, Idempotency)를 클로저 팩토리 패턴으로 DI 전환
- database.DB/RDB 전역 변수 제거, ConnectMySQL/Redis 값 반환으로 변경
- download API X-API-Version 헤더 + 하위 호환성 규칙 문서화
- SaveGameData PlayTimeDelta 원자적 UPDATE (race condition 해소)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

pkg/database/redis.go

@@ -7,14 +7,13 @@ import (
 	"github.com/redis/go-redis/v9"
 )
 
-// TODO: Consider injecting RDB as a dependency instead of using a package-level global
-// to improve testability. Currently, middleware directly accesses this global.
-var RDB *redis.Client
-
-func ConnectRedis() error {
-	RDB = redis.NewClient(&redis.Options{
+func ConnectRedis() (*redis.Client, error) {
+	rdb := redis.NewClient(&redis.Options{
 		Addr:     config.C.RedisAddr,
 		Password: config.C.RedisPassword,
 	})
-	return RDB.Ping(context.Background()).Err()
+	if err := rdb.Ping(context.Background()).Err(); err != nil {
+		return nil, err
+	}
+	return rdb, nil
 }