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 (
    12570, 12578, 12568, 12547, 12569, 12584, 
    12592, 12575, 12574, 12550, 12544, 
    12564, 12577, 12579, 12555, 12560, 
    12556, 12561, 12572, 12583, 12591, 
    12582, 12590, 12571, 12632, 12559, 
    12631, 10596, 10597, 10598, 10599, 
    10600
  ) 
  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 0.00062

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 (12570,12578,12568,12547,12569,12584,12592,12575,12574,12550,12544,12564,12577,12579,12555,12560,12556,12561,12572,12583,12591,12582,12590,12571,12632,12559,12631,10596,10597,10598,10599,10600) 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)"
    }
  }
}