SELECT 
  a.category_id 
FROM 
  cscart_categories as a 
  LEFT JOIN cscart_categories as b ON b.category_id IN (644) 
WHERE 
  a.id_path LIKE CONCAT(b.id_path, '/%')

Query time 0.00769

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "368.89"
    },
    "nested_loop": [
      {
        "table": {
          "table_name": "b",
          "access_type": "const",
          "possible_keys": [
            "PRIMARY",
            "p_category_id"
          ],
          "key": "PRIMARY",
          "used_key_parts": [
            "category_id"
          ],
          "key_length": "3",
          "ref": [
            "const"
          ],
          "rows_examined_per_scan": 1,
          "rows_produced_per_join": 1,
          "filtered": "100.00",
          "cost_info": {
            "read_cost": "0.00",
            "eval_cost": "0.10",
            "prefix_cost": "0.00",
            "data_read_per_join": "3K"
          },
          "used_columns": [
            "category_id",
            "id_path"
          ]
        }
      },
      {
        "table": {
          "table_name": "a",
          "access_type": "ALL",
          "rows_examined_per_scan": 3444,
          "rows_produced_per_join": 382,
          "filtered": "11.11",
          "cost_info": {
            "read_cost": "24.49",
            "eval_cost": "38.26",
            "prefix_cost": "368.89",
            "data_read_per_join": "1M"
          },
          "used_columns": [
            "category_id",
            "id_path"
          ],
          "attached_condition": "(`s2cart`.`a`.`id_path` like <cache>(concat('644','/%')))"
        }
      }
    ]
  }
}

Result

category_id
690
659
660
661
662
663
664
665
666
667
680
681
682
683
684
685
686
687
688
689
658
657
656
655
654
653
652
651
650
649
648
646
647
645
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757