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/mysql.go

@@ -9,28 +9,23 @@ import (
 	"gorm.io/gorm"
 )
 
-// TODO: Consider injecting DB as a dependency instead of using a package-level global
-// to improve testability. Currently, middleware directly accesses this global.
-var DB *gorm.DB
-
-func ConnectMySQL() error {
+func ConnectMySQL() (*gorm.DB, error) {
 	c := config.C
 	dsn := fmt.Sprintf("%s:%s@tcp(%s:%s)/%s?charset=utf8mb4&parseTime=True&loc=Local",
 		c.DBUser, c.DBPassword, c.DBHost, c.DBPort, c.DBName,
 	)
 	db, err := gorm.Open(mysql.Open(dsn), &gorm.Config{})
 	if err != nil {
-		return err
+		return nil, err
 	}
 
 	sqlDB, err := db.DB()
 	if err != nil {
-		return fmt.Errorf("sql.DB 획득 실패: %w", err)
+		return nil, fmt.Errorf("sql.DB 획득 실패: %w", err)
 	}
 	sqlDB.SetMaxOpenConns(25)
 	sqlDB.SetMaxIdleConns(10)
 	sqlDB.SetConnMaxLifetime(5 * time.Minute)
 
-	DB = db
-	return nil
+	return db, nil
 }