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 (
    1446, 2276, 1754, 1755, 529, 2051, 595, 
    594, 2593, 662, 876, 877, 880, 881, 882, 
    883, 949, 2882, 346, 952
  ) 
  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 0.00099

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "28.01"
    },
    "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": 40,
      "rows_produced_per_join": 40,
      "filtered": "100.00",
      "index_condition": "((`zdrowy_db`.`cscart_seo_names`.`object_id` in (1446,2276,1754,1755,529,2051,595,594,2593,662,876,877,880,881,882,883,949,2882,346,952)) and (`zdrowy_db`.`cscart_seo_names`.`type` = 'p') and (`zdrowy_db`.`cscart_seo_names`.`dispatch` = '') and (`zdrowy_db`.`cscart_seo_names`.`lang_code` = 'ru') and ((`zdrowy_db`.`cscart_seo_names`.`company_id` = 1) or (`zdrowy_db`.`cscart_seo_names`.`company_id` = 0)))",
      "cost_info": {
        "read_cost": "24.01",
        "eval_cost": "4.00",
        "prefix_cost": "28.01",
        "data_read_per_join": "67K"
      },
      "used_columns": [
        "name",
        "object_id",
        "company_id",
        "type",
        "dispatch",
        "path",
        "lang_code"
      ]
    }
  }
}

Result

product_id seo_name seo_path
346 22h23-polotenca-slozhenie-v-25-250-listov-rossiya 315/322
529 zubnaya-schetka-a-13-klasik-h12-grendi 315/320
594 kosmeticheskie-salfetki-belux-60-l.-3-sl.-belye-h20 315/378
595 kosmeticheskie-salfetki-belux-80-l.-2-sl.-belye-h20 315/378
662 mylnica-dorozhnaya-110h70h38 315/320
876 platochki-belux-3sl 315/321
877 platochki-belux-plus-3sl 315/321
880 platochki-semya-i-komfort-3-h-sl-aloe-h10 315/321
881 platochki-semya-i-komfort-3-h-sl.-siren-h10 315/321
882 platochki-semya-i-komfort-3-h-sl.-ekzotik-h10 315/321
883 platochki-semya-i-komfort-3-h-sl.belye-h10 315/321
949 polotenca-3v1-belux-1sht-2sl-belye 315/322
952 polotenca-bumazhnye-belux-big-rol-2sl.-1sht-h6 315/322
1446 bumazhnye-salfetki-premium-evrostandart-24h24-1-sloy-90-listov-pachka-belye-30 315/323
1754 zubnaya-schetka-grendy-d-48-mashinka-1-12 315/320
1755 zubnaya-schetka-grendy-v-24-zigzag-plyus-1-12 315/320
2051 zubnaya-schetka-mod-assorti-v-pakete-art-917 315/320
2276 vlazhnye-salfetki-aura-d-detey-ultra-comfort-15-sht-10-110 315/317
2593 kosmeticheskie-salfetki-semya-i-komfort-100l-2-sl-belye 315/378
2882 polotenca-v-slozhenie-150-listov-20-upak-korob-rossiya 315/322