SELECT 
  cscart_products_categories.product_id, 
  GROUP_CONCAT(
    IF(
      cscart_products_categories.link_type = "M", 
      CONCAT(
        cscart_products_categories.category_id, 
        "M"
      ), 
      cscart_products_categories.category_id
    )
  ) AS category_ids 
FROM 
  cscart_products_categories 
  INNER JOIN cscart_categories ON cscart_categories.category_id = cscart_products_categories.category_id 
  AND cscart_categories.storefront_id IN (0, 1) 
  AND (
    cscart_categories.usergroup_ids = '' 
    OR FIND_IN_SET(
      0, cscart_categories.usergroup_ids
    ) 
    OR FIND_IN_SET(
      1, cscart_categories.usergroup_ids
    )
  ) 
  AND cscart_categories.status IN ('A', 'H') 
WHERE 
  cscart_products_categories.product_id IN (
    51272, 51271, 51270, 51269, 51268, 51267, 
    51266, 145, 14, 113, 6, 51354, 51353, 
    43, 51356, 51355, 44
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00104

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "50.66"
    },
    "grouping_operation": {
      "using_filesort": false,
      "nested_loop": [
        {
          "table": {
            "table_name": "cscart_products_categories",
            "access_type": "range",
            "possible_keys": [
              "PRIMARY",
              "pt"
            ],
            "key": "pt",
            "used_key_parts": [
              "product_id"
            ],
            "key_length": "3",
            "rows_examined_per_scan": 58,
            "rows_produced_per_join": 58,
            "filtered": "100.00",
            "index_condition": "(`test_uchur_k`.`cscart_products_categories`.`product_id` in (51272,51271,51270,51269,51268,51267,51266,145,14,113,6,51354,51353,43,51356,51355,44))",
            "cost_info": {
              "read_cost": "24.56",
              "eval_cost": "5.80",
              "prefix_cost": "30.36",
              "data_read_per_join": "928"
            },
            "used_columns": [
              "product_id",
              "category_id",
              "link_type"
            ]
          }
        },
        {
          "table": {
            "table_name": "cscart_categories",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "c_status",
              "p_category_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "category_id"
            ],
            "key_length": "3",
            "ref": [
              "test_uchur_k.cscart_products_categories.category_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 2,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "14.50",
              "eval_cost": "0.29",
              "prefix_cost": "50.66",
              "data_read_per_join": "15K"
            },
            "used_columns": [
              "category_id",
              "storefront_id",
              "usergroup_ids",
              "status"
            ],
            "attached_condition": "((`test_uchur_k`.`cscart_categories`.`storefront_id` in (0,1)) and ((`test_uchur_k`.`cscart_categories`.`usergroup_ids` = '') or (0 <> find_in_set(0,`test_uchur_k`.`cscart_categories`.`usergroup_ids`)) or (0 <> find_in_set(1,`test_uchur_k`.`cscart_categories`.`usergroup_ids`))) and (`test_uchur_k`.`cscart_categories`.`status` in ('A','H')))"
          }
        }
      ]
    }
  }
}

Result

product_id category_ids
6 6,42,40M
14 6,42,40M
43 20,44,40M
44 20,43,40M
113 6,42,40M
145 42,7,390,40M
51266 390,42,7,40M
51267 390,7,42,40M
51268 390,42,7,40M
51269 42,7,390,40M
51270 7,390,42,40M
51271 390,42,7,40M
51272 42,390,7,40M
51353 44,20,40M
51354 44,20,40M
51355 43,20,40M
51356 43,20,40M