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 (
    848, 590, 859, 828, 842, 857, 879, 839, 
    868, 852, 873, 591
  ) 
  AND cscart_seo_names.type = "p" 
  AND cscart_seo_names.dispatch = "" 
  AND cscart_seo_names.lang_code = 'ru'

Query time 0.00056

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "28.81"
    },
    "table": {
      "table_name": "cscart_seo_names",
      "access_type": "range",
      "possible_keys": [
        "PRIMARY",
        "dispatch"
      ],
      "key": "PRIMARY",
      "used_key_parts": [
        "object_id",
        "type",
        "dispatch",
        "lang_code"
      ],
      "key_length": "206",
      "rows_examined_per_scan": 12,
      "rows_produced_per_join": 12,
      "filtered": "100.00",
      "index_condition": "((`cscart`.`cscart_seo_names`.`object_id` in (848,590,859,828,842,857,879,839,868,852,873,591)) and (`cscart`.`cscart_seo_names`.`type` = 'p') and (`cscart`.`cscart_seo_names`.`dispatch` = '') and (`cscart`.`cscart_seo_names`.`lang_code` = 'ru'))",
      "cost_info": {
        "read_cost": "26.41",
        "eval_cost": "2.40",
        "prefix_cost": "28.81",
        "data_read_per_join": "20K"
      },
      "used_columns": [
        "name",
        "object_id",
        "type",
        "dispatch",
        "path",
        "lang_code"
      ]
    }
  }
}

Result

product_id seo_name seo_path
590 krovat-s-podemnym-mehanizmom-avangard 301/302
591 krovat-s-podemnym-mehanizmom-mone 301/302
828 krovat-s-podemnym-mehanizmom-brianna 301/302/367
839 krovat-s-podemnym-mehanizmom-dakota 301/302/368
842 krovat-s-podemnym-mehanizmom-brianna 301/302/368
848 krovat-aleks 301/302/368
852 krovat-s-podemnym-mehanizmom-kassiya 301/302/369
857 krovat-s-podemnym-mehanizmom-brianna 301/302/369
859 krovat-s-podemnym-mehanizmom-muza 301/302/369
868 krovat-s-podemnym-mehanizmom-dakota 301/302/369
873 krovat-s-podemnym-mehanizmom-lyuksor 301/302/370
879 krovat-s-podemnym-mehanizmom-vittoriya 301/302/371