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 (
    7063, 9852, 10334, 7496, 10707, 10352, 
    10042, 10521, 10506, 10618, 10040, 
    12456, 12457, 7550, 10518, 10353, 7566, 
    10517, 7648, 7146, 10272, 10273, 10091, 
    7252
  ) 
  AND cscart_seo_names.type = "p" 
  AND cscart_seo_names.dispatch = "" 
  AND cscart_seo_names.lang_code = 'uk' 
  AND (
    cscart_seo_names.company_id = 1 
    OR cscart_seo_names.company_id = 0
  )

Query time 0.00090

JSON explain

{
  "query_block": {
    "select_id": 1,
    "nested_loop": [
      {
        "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": 48,
          "filtered": 100,
          "index_condition": "cscart_seo_names.object_id in (7063,9852,10334,7496,10707,10352,10042,10521,10506,10618,10040,12456,12457,7550,10518,10353,7566,10517,7648,7146,10272,10273,10091,7252) and cscart_seo_names.`type` = 'p' and cscart_seo_names.dispatch = '' and cscart_seo_names.lang_code = 'uk' and (cscart_seo_names.company_id = 1 or cscart_seo_names.company_id = 0)"
        }
      }
    ]
  }
}

Result

product_id seo_name seo_path
7063 palichki-apelsinovi-11-sm-100-sht 397/543
7146 kist-dlya-tonu-i-korektora-ribka-zolota 393/561
7252 kist-transformer-dlya-gelyu-6-skoshena 393/577
7496 palichki-apelsinovi-100-sht-18-sm 397/543
7550 kist-dlya-gelyu-zharptica 393/577
7566 kist-dlya-gelyu-z-kristalami-8 393/577
7648 kist-dlya-malyuvannya-opi-kolinsky-3 393/552
9852 palichki-apelsinovi-14-sm-100-sht 397/543
10040 kist-dlya-briv 393/561
10042 penzel-global-skosheniy 393/577
10091 kist-kosmetologichna-dlya-nanesennya-masok 404/563
10272 kist-dlya-tonu-i-korektora-ribka-kolorova 393/561
10273 kist-dlya-tonu-i-korektora-ribka-sriblo 393/561
10334 palichki-apelsinovi-7-sm-100-sht 397/543
10352 patchi-pid-ochi-dlya-naroschuvannya-viy 399/604
10353 kist-dlya-gelyu-opi-kolinsky-4 393/577
10506 penzel-dlya-akril-gelyu-chorniy 393/577
10517 kist-dlya-gradiienta-ombre 393/552
10518 kist-dlya-gelyu-zi-strazami-2-blakitna 393/577
10521 penzel-z-kristalami-siniy-15-mm 393/552
10618 kist-dlya-gelyu-rusalka 393/577
10707 papir-dlya-depilyacii-v-ruloni-100-m 402/700
12456 profesiyna-kist-dlya-briv 393/561
12457 kist-dlya-briv-skoshena 393/561