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 (
    13006, 13005, 13004, 13003, 13002, 13001, 
    13000, 12999, 10812, 10811, 10810, 
    10809, 10808, 10807, 10806, 10805, 
    10804, 10803, 10802, 10801
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00056

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "cscart_products_categories",
      "access_type": "range",
      "possible_keys": ["PRIMARY", "pt"],
      "key": "pt",
      "key_length": "3",
      "used_key_parts": ["product_id"],
      "rows": 20,
      "filtered": 100,
      "index_condition": "cscart_products_categories.product_id in (13006,13005,13004,13003,13002,13001,13000,12999,10812,10811,10810,10809,10808,10807,10806,10805,10804,10803,10802,10801)"
    },
    "table": {
      "table_name": "cscart_categories",
      "access_type": "eq_ref",
      "possible_keys": ["PRIMARY", "c_status", "p_category_id"],
      "key": "PRIMARY",
      "key_length": "3",
      "used_key_parts": ["category_id"],
      "ref": ["noframes_angrybeaver.cscart_products_categories.category_id"],
      "rows": 1,
      "filtered": 100,
      "attached_condition": "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')"
    }
  }
}

Result

product_id category_ids
10801 1676M
10802 1676M
10803 1676M
10804 1676M
10805 1676M
10806 1676M
10807 1676M
10808 1676M
10809 1676M
10810 1676M
10811 1676M
10812 1676M
12999 1682,301M
13000 1682,301M
13001 1682,301M
13002 1682,301M
13003 1682,301M
13004 1682,301M
13005 1682,301M
13006 1682,301M