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 = 346 
WHERE 
  cscart_products_categories.product_id IN (
    870, 1797, 1652, 2809, 1427, 1083, 1084, 
    2627, 2628, 2817, 2810, 1181, 1725, 
    1726, 1727, 2130, 1537, 1538, 1539, 
    1396
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00128

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "29.16"
    },
    "grouping_operation": {
      "using_filesort": false,
      "nested_loop": [
        {
          "table": {
            "table_name": "cscart_products_categories",
            "access_type": "range",
            "possible_keys": [
              "PRIMARY",
              "pt"
            ],
            "key": "pt",
            "used_key_parts": [
              "product_id"
            ],
            "key_length": "3",
            "rows_examined_per_scan": 21,
            "rows_produced_per_join": 21,
            "filtered": "100.00",
            "index_condition": "(`zdrowy_db`.`cscart_products_categories`.`product_id` in (870,1797,1652,2809,1427,1083,1084,2627,2628,2817,2810,1181,1725,1726,1727,2130,1537,1538,1539,1396))",
            "cost_info": {
              "read_cost": "12.36",
              "eval_cost": "2.10",
              "prefix_cost": "14.46",
              "data_read_per_join": "336"
            },
            "used_columns": [
              "product_id",
              "category_id",
              "link_type"
            ]
          }
        },
        {
          "table": {
            "table_name": "product_position_source",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "pt"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "category_id",
              "product_id"
            ],
            "key_length": "6",
            "ref": [
              "const",
              "zdrowy_db.cscart_products_categories.product_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 21,
            "filtered": "100.00",
            "cost_info": {
              "read_cost": "5.25",
              "eval_cost": "2.10",
              "prefix_cost": "21.81",
              "data_read_per_join": "336"
            },
            "used_columns": [
              "product_id",
              "category_id",
              "position"
            ]
          }
        },
        {
          "table": {
            "table_name": "cscart_categories",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "c_status",
              "p_category_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "category_id"
            ],
            "key_length": "3",
            "ref": [
              "zdrowy_db.cscart_products_categories.category_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 1,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "5.25",
              "eval_cost": "0.11",
              "prefix_cost": "29.16",
              "data_read_per_join": "6K"
            },
            "used_columns": [
              "category_id",
              "usergroup_ids",
              "status",
              "storefront_id"
            ],
            "attached_condition": "((`zdrowy_db`.`cscart_categories`.`storefront_id` in (0,1)) and ((`zdrowy_db`.`cscart_categories`.`usergroup_ids` = '') or (0 <> find_in_set(0,`zdrowy_db`.`cscart_categories`.`usergroup_ids`)) or (0 <> find_in_set(1,`zdrowy_db`.`cscart_categories`.`usergroup_ids`))) and (`zdrowy_db`.`cscart_categories`.`status` in ('A','H')))"
          }
        }
      ]
    }
  }
}

Result

product_id category_ids position
870 347M
1083 348M
1084 348M
1181 349M
1396 349M
1427 348M
1537 349M
1538 349M
1539 349M
1652 347M
1725 349M
1726 349M
1727 349M
1797 347M
2130 349M
2627 349M
2628 349M
2809 347M
2810 349M
2817 349M