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 (
    22421, 22424, 22290, 50981, 50982, 50983, 
    51416, 51421, 51413, 51412, 51054
  ) 
  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 0.00060

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "15.41"
    },
    "table": {
      "table_name": "cscart_seo_names",
      "access_type": "range",
      "possible_keys": [
        "PRIMARY",
        "dispatch"
      ],
      "key": "PRIMARY",
      "used_key_parts": [
        "object_id",
        "type",
        "dispatch",
        "lang_code",
        "company_id"
      ],
      "key_length": "210",
      "rows_examined_per_scan": 22,
      "rows_produced_per_join": 22,
      "filtered": "100.00",
      "index_condition": "((`test_uchur_k`.`cscart_seo_names`.`object_id` in (22421,22424,22290,50981,50982,50983,51416,51421,51413,51412,51054)) and (`test_uchur_k`.`cscart_seo_names`.`type` = 'p') and (`test_uchur_k`.`cscart_seo_names`.`dispatch` = '') and (`test_uchur_k`.`cscart_seo_names`.`lang_code` = 'ru') and ((`test_uchur_k`.`cscart_seo_names`.`company_id` = 1) or (`test_uchur_k`.`cscart_seo_names`.`company_id` = 0)))",
      "cost_info": {
        "read_cost": "13.21",
        "eval_cost": "2.20",
        "prefix_cost": "15.41",
        "data_read_per_join": "37K"
      },
      "used_columns": [
        "name",
        "object_id",
        "company_id",
        "type",
        "dispatch",
        "path",
        "lang_code"
      ]
    }
  }
}

Result

product_id seo_name seo_path
22290 nozh-yakutskiy-stal-65g-rukoyat-listvennica-master-vasilev-leonid-stepanovich 2/133
22421 nozh-yakutskiy-uchur-stal-hvg-rukoyat-karagach-nozhny-kozha-sredniy-master-bilyukin-saryal 2/133
22424 nozh-yakutskiy-uchur-stal-65g-rukoyat-karagach-nozhny-kozha-sredniy-master-bilyukin-saryal 2/133
50981 yakutskiy-nozh-st95h18-ruk-kov-ber-kozh-cheh 2/133
50982 nozh-yakutskiy-s-kovannoy-doloy-i-golovoy-medvedya 2/133
50983 nozh-yakutskiy-uchur-stal-65g-rukoyat-karagach-nozhny-kozha-bolshoy-master-bilyukin-saryal 2/133
51054 tochilka-ruixin-pro-3-rx-003 2/133
51412 nozh-morakniv-outdoor-2000-orange 2/133
51413 nozh-morakniv-outdoor-2000-green 2/133
51416 nozh-morakniv-pro-c 2/133
51421 nozh-morakniv-companion-spark-blue 2/133