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 (
    12500, 10200, 10201, 10566, 10545, 10227, 
    10552, 12506, 10693, 12508, 9953, 12522, 
    12507, 12498, 13101, 13100, 10699, 
    10695, 10195, 10576, 10696, 9760, 10583, 
    10701, 10582, 10139, 12503, 10575, 
    9932, 10075, 10135, 9952
  ) 
  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 0.00107

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 (12500,10200,10201,10566,10545,10227,10552,12506,10693,12508,9953,12522,12507,12498,13101,13100,10699,10695,10195,10576,10696,9760,10583,10701,10582,10139,12503,10575,9932,10075,10135,9952) 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)"
    }
  }
}