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 (
    12568, 10261, 10260, 10259, 10258, 10257, 
    10256, 10255, 10254, 10253, 10252, 
    10251, 10250, 10249, 10248, 10247, 
    10246, 10245, 10244, 10243
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00075

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": 21,
      "filtered": 100,
      "index_condition": "cscart_products_categories.product_id in (12568,10261,10260,10259,10258,10257,10256,10255,10254,10253,10252,10251,10250,10249,10248,10247,10246,10245,10244,10243)"
    },
    "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
10243 1622M
10244 1622M
10245 1622M
10246 1622M
10247 1622M
10248 1622M
10249 1622M
10250 1622M
10251 1622M
10252 1622M
10253 1622M
10254 1622M
10255 1622M
10256 1622M
10257 1622M
10258 1622M
10259 1622M
10260 1622M
10261 1622M
12568 267,278,277M