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 (
    596, 597, 601, 602, 603, 604, 678, 679, 
    680
  ) 
  AND cscart_seo_names.type = "p" 
  AND cscart_seo_names.dispatch = "" 
  AND cscart_seo_names.lang_code = 'ru'

Query time 0.00042

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "21.61"
    },
    "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": 9,
      "rows_produced_per_join": 9,
      "filtered": "100.00",
      "index_condition": "((`cscart`.`cscart_seo_names`.`object_id` in (596,597,601,602,603,604,678,679,680)) 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": "19.81",
        "eval_cost": "1.80",
        "prefix_cost": "21.61",
        "data_read_per_join": "15K"
      },
      "used_columns": [
        "name",
        "object_id",
        "type",
        "dispatch",
        "path",
        "lang_code"
      ]
    }
  }
}

Result

product_id seo_name seo_path
596 shkaf-dzhelato-dub-vinchenca-beton-kashemir 303/304
597 shkaf-dzhelato-dub-vinchenca-beton-kashemir-ru 303/304
601 stellazh-pravyy-dzhelato-dub-vinchenca-shampan 303/305
602 stellazh-pravyy-dzhelato-dub-vinchenca-shampan-ru 303/305
603 stellazh-levyy-dzhelato-dub-vinchenca-shampan 303/305
604 stellazh-levyy-dzhelato-dub-vinchenca-shampan-ru 303/305
678 mini-prihozhaya-ivet-dub-zolotistyy-ru 303/304
679 mini-prihozhaya-ivet-dub-zolotistyy 303
680 mini-prihozhaya-ivet-dub-zolotistyy-ru-2 303/304