SELECT 
  * 
FROM 
  cscart_mb_salvage_cases 
WHERE 
  auction_product_id IN (
    10566, 10567, 10572, 10575, 10581, 10582, 
    10583, 10584, 10588, 10589, 10590, 
    10595, 10596, 10602, 10612, 10613
  ) 
  OR sale_product_id IN (
    10566, 10567, 10572, 10575, 10581, 10582, 
    10583, 10584, 10588, 10589, 10590, 
    10595, 10596, 10602, 10612, 10613
  ) 
ORDER BY 
  updated_at DESC, 
  case_id DESC

Query time 0.00032

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 (10566,10567,10572,10575,10581,10582,10583,10584,10588,10589,10590,10595,10596,10602,10612,10613) or cscart_mb_salvage_cases.sale_product_id in (10566,10567,10572,10575,10581,10582,10583,10584,10588,10589,10590,10595,10596,10602,10612,10613)"
        }
      }
    }
  }
}