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 = 1629 
WHERE 
  cscart_products_categories.product_id IN (
    10063, 10052, 10072, 10046, 10059, 10064, 
    10057, 10048, 10062, 10070, 10058, 
    10045, 10054, 10071, 10067, 10051, 
    10060, 10055, 10043, 10068
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00063

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 (10063,10052,10072,10046,10059,10064,10057,10048,10062,10070,10058,10045,10054,10071,10067,10051,10060,10055,10043,10068)"
    },
    "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
10043 1629M 0
10045 1629M 0
10046 1629M 0
10048 1629M 0
10051 1629M 0
10052 1629M 0
10054 1629M 0
10055 1629M 0
10057 1629M 0
10058 1629M 0
10059 1629M 0
10060 1629M 0
10062 1629M 0
10063 1629M 0
10064 1629M 0
10067 1629M 0
10068 1629M 0
10070 1629M 0
10071 1629M 0
10072 1629M 0