SELECT 
  products_categories.product_id, 
  GROUP_CONCAT(
    IF(
      products_categories.link_type = "M", 
      CONCAT(
        products_categories.category_id, 
        "M"
      ), 
      products_categories.category_id
    )
  ) AS category_ids 
FROM 
  products_categories 
  INNER JOIN categories ON categories.category_id = products_categories.category_id 
  AND categories.storefront_id IN (0, 1) 
  AND (
    categories.usergroup_ids = '' 
    OR FIND_IN_SET(0, categories.usergroup_ids) 
    OR FIND_IN_SET(1, categories.usergroup_ids)
  ) 
  AND categories.status IN ('A', 'H') 
WHERE 
  products_categories.product_id IN (
    259571, 252628, 259568, 252613, 252659, 
    252689, 264799, 252606, 252604, 252600, 
    252684, 264803
  ) 
GROUP BY 
  products_categories.product_id

Query time 0.00096

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "25.60"
    },
    "grouping_operation": {
      "using_filesort": false,
      "nested_loop": [
        {
          "table": {
            "table_name": "products_categories",
            "access_type": "range",
            "possible_keys": [
              "PRIMARY",
              "link_type",
              "pt"
            ],
            "key": "pt",
            "used_key_parts": [
              "product_id"
            ],
            "key_length": "3",
            "rows_examined_per_scan": 46,
            "rows_produced_per_join": 46,
            "filtered": "100.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "4.90",
              "eval_cost": "4.60",
              "prefix_cost": "9.50",
              "data_read_per_join": "736"
            },
            "used_columns": [
              "product_id",
              "category_id",
              "link_type"
            ],
            "attached_condition": "(`goimagine`.`products_categories`.`product_id` in (259571,252628,259568,252613,252659,252689,264799,252606,252604,252600,252684,264803))"
          }
        },
        {
          "table": {
            "table_name": "categories",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "c_status",
              "p_category_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "category_id"
            ],
            "key_length": "3",
            "ref": [
              "goimagine.products_categories.category_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 2,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "11.50",
              "eval_cost": "0.23",
              "prefix_cost": "25.60",
              "data_read_per_join": "6K"
            },
            "used_columns": [
              "category_id",
              "usergroup_ids",
              "status",
              "storefront_id"
            ],
            "attached_condition": "((`goimagine`.`categories`.`storefront_id` in (0,1)) and ((`goimagine`.`categories`.`usergroup_ids` = '') or (0 <> find_in_set(0,`goimagine`.`categories`.`usergroup_ids`)) or (0 <> find_in_set(1,`goimagine`.`categories`.`usergroup_ids`))) and (`goimagine`.`categories`.`status` in ('A','H')))"
          }
        }
      ]
    }
  }
}

Result

product_id category_ids
252600 17805,18649,18682,2566M
252604 17805,18662,18709,2566M
252606 18758,18759,2566M
252613 18765,18766,18769,2566M
252628 18758,18759,2566M
252659 18758,18759,2566M
252684 18772,18786,2566M
252689 17805,18641,18642,2566M
259568 17805,18661,18727,2566M
259571 17805,18661,18727,2566M
264799 17805,18641,18648,18761,2566M
264803 17805,18641,18647,18746,2566M