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 (
    565, 564, 567, 566, 572, 571, 570, 569, 
    568, 573, 574, 575, 576, 577, 578, 579, 
    580, 581, 582, 583, 584, 585, 586
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00078

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "106.91"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "cost_info": {
        "sort_cost": "2.82"
      },
      "nested_loop": [
        {
          "table": {
            "table_name": "cscart_categories",
            "access_type": "ALL",
            "possible_keys": [
              "PRIMARY",
              "c_status",
              "p_category_id"
            ],
            "rows_examined_per_scan": 125,
            "rows_produced_per_join": 5,
            "filtered": "4.00",
            "cost_info": {
              "read_cost": "29.49",
              "eval_cost": "1.00",
              "prefix_cost": "30.49",
              "data_read_per_join": "20K"
            },
            "used_columns": [
              "category_id",
              "storefront_id",
              "usergroup_ids",
              "status"
            ],
            "attached_condition": "((`cscart`.`cscart_categories`.`storefront_id` in (0,1)) and ((`cscart`.`cscart_categories`.`usergroup_ids` = '') or find_in_set(0,`cscart`.`cscart_categories`.`usergroup_ids`) or find_in_set(1,`cscart`.`cscart_categories`.`usergroup_ids`)) and (`cscart`.`cscart_categories`.`status` in ('A','H')))"
          }
        },
        {
          "table": {
            "table_name": "cscart_products_categories",
            "access_type": "ref",
            "possible_keys": [
              "PRIMARY",
              "pt"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "category_id"
            ],
            "key_length": "3",
            "ref": [
              "cscart.cscart_categories.category_id"
            ],
            "rows_examined_per_scan": 12,
            "rows_produced_per_join": 2,
            "filtered": "4.71",
            "index_condition": "(`cscart`.`cscart_products_categories`.`product_id` in (565,564,567,566,572,571,570,569,568,573,574,575,576,577,578,579,580,581,582,583,584,585,586))",
            "cost_info": {
              "read_cost": "61.60",
              "eval_cost": "0.56",
              "prefix_cost": "104.09",
              "data_read_per_join": "45"
            },
            "used_columns": [
              "product_id",
              "category_id",
              "link_type"
            ]
          }
        }
      ]
    }
  }
}

Result

product_id category_ids
564 389,300M
565 389,300M
566 389,300M
567 389,300M
568 300M,388
569 300M,388
570 300M,388
571 300M,388
572 300M,388
573 388,403,300M
574 300M,388,403
575 300M,388,403
576 300M,388,403
577 300M,388,403
578 389,300M,403
579 389,300M,403
580 403,389,300M
581 300M,403,389
582 300M,403,389
583 300M,403,388
584 300M,403,388
585 388,300M,403
586 403,388,300M