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, 
  product_position_source.position AS position 
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') 
  LEFT JOIN cscart_products_categories AS product_position_source ON cscart_products_categories.product_id = product_position_source.product_id 
  AND product_position_source.category_id = 265 
WHERE 
  cscart_products_categories.product_id IN (
    12616, 12601, 12628, 12602, 12640, 12647, 
    12588, 12605, 12606, 12637, 12612, 
    12613, 12641, 12554, 12552, 12642
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00365

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": 32,
      "filtered": 100,
      "index_condition": "cscart_products_categories.product_id in (12616,12601,12628,12602,12640,12647,12588,12605,12606,12637,12612,12613,12641,12554,12552,12642)"
    },
    "table": {
      "table_name": "product_position_source",
      "access_type": "eq_ref",
      "possible_keys": ["PRIMARY", "pt"],
      "key": "PRIMARY",
      "key_length": "6",
      "used_key_parts": ["category_id", "product_id"],
      "ref": [
        "const",
        "noframes_angrybeaver.cscart_products_categories.product_id"
      ],
      "rows": 1,
      "filtered": 100
    },
    "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 position
12552 267,270,268M
12554 267,270,268M
12588 285,270,267M
12601 267,270,277M
12602 270,277,267M
12605 267,277,270M
12606 277,270,267M
12612 270,267,277M
12613 270,267,277M
12616 277,270,267M
12628 267,277,270M
12637 277,267,270M
12640 270,277,285,267M
12641 277,270,285,267M
12642 277,267,285,270M
12647 277,270,285,267M