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 (
    10071, 10067, 10051, 10060, 10055, 10043, 
    10068, 10065, 10061, 10050, 10056, 
    10044, 10069, 10066, 12671, 12672, 
    15779, 12673, 12674, 12675, 12676, 
    12677, 12678, 12679, 9687, 10024, 10025, 
    10026, 10027, 10028, 10029, 10030
  ) 
  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 0.00081

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 (10071,10067,10051,10060,10055,10043,10068,10065,10061,10050,10056,10044,10069,10066,12671,12672,15779,12673,12674,12675,12676,12677,12678,12679,9687,10024,10025,10026,10027,10028,10029,10030) 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)"
    }
  }
}