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 (
    12616, 12599, 10666, 10664, 10663, 10661, 
    10659, 10658, 10657, 12619, 12620, 
    12593, 12595, 12585, 12587, 12623, 
    13091, 12588, 12590, 12591
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00058

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": 33,
      "filtered": 100,
      "index_condition": "cscart_products_categories.product_id in (12616,12599,10666,10664,10663,10661,10659,10658,10657,12619,12620,12593,12595,12585,12587,12623,13091,12588,12590,12591)"
    },
    "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
10657 275M
10658 275M
10659 275M
10661 275M
10663 275M
10664 275M
10666 275M
12585 270,267,1688M
12587 270,267,1688M
12588 285,270,267M
12590 267,278,277M
12591 277,267,278M
12593 270,267,1688M
12595 270,267,1688M
12599 277,267,270M
12616 277,270,267M
12619 267,270,1688M
12620 270,1688,267M
12623 267,1688,270M
13091 285,270,267M