SELECT 
  * 
FROM 
  cscart_mb_salvage_cases 
WHERE 
  auction_product_id IN (
    10680, 10681, 10682, 10683, 10684, 10685, 
    10686, 10687, 10688, 10692, 10693, 
    10694, 10699, 10702, 10704, 10705
  ) 
  OR sale_product_id IN (
    10680, 10681, 10682, 10683, 10684, 10685, 
    10686, 10687, 10688, 10692, 10693, 
    10694, 10699, 10702, 10704, 10705
  ) 
ORDER BY 
  updated_at DESC, 
  case_id DESC

Query time 0.00030

JSON explain

{
  "query_block": {
    "select_id": 1,
    "read_sorted_file": {
      "filesort": {
        "sort_key": "cscart_mb_salvage_cases.updated_at desc, cscart_mb_salvage_cases.case_id desc",
        "table": {
          "table_name": "cscart_mb_salvage_cases",
          "access_type": "ALL",
          "rows": 58,
          "filtered": 100,
          "attached_condition": "cscart_mb_salvage_cases.auction_product_id in (10680,10681,10682,10683,10684,10685,10686,10687,10688,10692,10693,10694,10699,10702,10704,10705) or cscart_mb_salvage_cases.sale_product_id in (10680,10681,10682,10683,10684,10685,10686,10687,10688,10692,10693,10694,10699,10702,10704,10705)"
        }
      }
    }
  }
}