SELECT 
  cscart_seo_names.object_id AS product_id, 
  cscart_seo_names.name AS seo_name, 
  cscart_seo_names.path AS seo_path 
FROM 
  cscart_seo_names 
WHERE 
  cscart_seo_names.object_id IN (
    10038, 10039, 10040, 10756, 10757, 10758, 
    10397, 10398, 10399, 10400, 10401, 
    10402, 12700, 10596, 10597, 10598, 
    10599, 10600, 10521, 10520, 10519, 
    10518, 10517, 10516, 10515, 10514, 
    10513, 10512, 10511, 10510, 10509, 
    10508
  ) 
  AND cscart_seo_names.type = "p" 
  AND cscart_seo_names.dispatch = "" 
  AND cscart_seo_names.lang_code = 'ru' 
  AND (
    cscart_seo_names.company_id = 1 
    OR cscart_seo_names.company_id = 0
  )

Query time 0.00116

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "cscart_seo_names",
      "access_type": "range",
      "possible_keys": ["PRIMARY", "dispatch"],
      "key": "PRIMARY",
      "key_length": "210",
      "used_key_parts": [
        "object_id",
        "type",
        "dispatch",
        "lang_code",
        "company_id"
      ],
      "rows": 64,
      "filtered": 100,
      "index_condition": "cscart_seo_names.object_id in (10038,10039,10040,10756,10757,10758,10397,10398,10399,10400,10401,10402,12700,10596,10597,10598,10599,10600,10521,10520,10519,10518,10517,10516,10515,10514,10513,10512,10511,10510,10509,10508) and cscart_seo_names.`type` = 'p' and cscart_seo_names.dispatch = '' and cscart_seo_names.lang_code = 'ru' and (cscart_seo_names.company_id = 1 or cscart_seo_names.company_id = 0)"
    }
  }
}