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 (
    451713, 405280, 458098, 422838, 435233, 
    411645, 422883, 427836, 459826, 446751, 
    417009, 400995
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00062

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost": 0.041504743,
    "nested_loop": [
      {
        "table": {
          "table_name": "cscart_products_categories",
          "access_type": "range",
          "possible_keys": ["PRIMARY", "pt"],
          "key": "pt",
          "key_length": "3",
          "used_key_parts": ["product_id"],
          "loops": 1,
          "rows": 12,
          "cost": 0.02230238,
          "filtered": 100,
          "attached_condition": "cscart_products_categories.product_id in (451713,405280,458098,422838,435233,411645,422883,427836,459826,446751,417009,400995)",
          "using_index": true
        }
      },
      {
        "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": ["u985510652_ecartify.cscart_products_categories.category_id"],
          "loops": 12,
          "rows": 1,
          "cost": 0.01155248,
          "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
400995 495M
405280 500M
411645 305M
417009 500M
422838 495M
422883 498M
427836 500M
435233 289M
446751 289M
451713 498M
458098 495M
459826 495M