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 (
    693, 682, 676, 673, 671, 670, 664, 663, 
    658, 657, 656, 651, 650, 647, 645, 644, 
    641, 639, 636, 624, 622, 620
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00101

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "12.31"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "cost_info": {
        "sort_cost": "2.45"
      },
      "nested_loop": [
        {
          "table": {
            "table_name": "cscart_categories",
            "access_type": "ALL",
            "possible_keys": [
              "PRIMARY",
              "c_status",
              "p_category_id"
            ],
            "rows_examined_per_scan": 20,
            "rows_produced_per_join": 1,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "2.52",
              "eval_cost": "0.10",
              "prefix_cost": "2.62",
              "data_read_per_join": "2K"
            },
            "used_columns": [
              "category_id",
              "usergroup_ids",
              "status",
              "storefront_id"
            ],
            "attached_condition": "((`betaatif_store`.`cscart_categories`.`storefront_id` in (0,1)) and ((`betaatif_store`.`cscart_categories`.`usergroup_ids` = '') or (0 <> find_in_set(0,`betaatif_store`.`cscart_categories`.`usergroup_ids`)) or (0 <> find_in_set(1,`betaatif_store`.`cscart_categories`.`usergroup_ids`))) and (`betaatif_store`.`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": [
              "betaatif_store.cscart_categories.category_id"
            ],
            "rows_examined_per_scan": 43,
            "rows_produced_per_join": 2,
            "filtered": "5.69",
            "index_condition": "(`betaatif_store`.`cscart_products_categories`.`product_id` in (693,682,676,673,671,670,664,663,658,657,656,651,650,647,645,644,641,639,636,624,622,620))",
            "cost_info": {
              "read_cost": "2.94",
              "eval_cost": "0.24",
              "prefix_cost": "9.86",
              "data_read_per_join": "39"
            },
            "used_columns": [
              "product_id",
              "category_id",
              "link_type"
            ]
          }
        }
      ]
    }
  }
}

Result

product_id category_ids
620 5M
622 5M
624 17M
636 2M,17
639 2M,17
641 2M,17
644 2M,17
645 18M
647 2,17M
650 17,2M
651 16M
656 15M,3
657 15M,3
658 15M,3
663 3,15M
664 15M,3
670 15M
671 15M
673 2M,17
676 5M
682 5M
693 5M