SELECT 
  a.category_id 
FROM 
  cscart_categories as a 
  LEFT JOIN cscart_categories as b ON b.category_id IN (313) 
WHERE 
  a.id_path LIKE CONCAT(b.id_path, '/%')

Query time 0.00021

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost": 0.060074355,
    "nested_loop": [
      {
        "table": {
          "table_name": "b",
          "access_type": "const",
          "possible_keys": ["PRIMARY", "p_category_id"],
          "key": "PRIMARY",
          "key_length": "3",
          "used_key_parts": ["category_id"],
          "ref": ["const"],
          "rows": 1,
          "filtered": 100
        }
      },
      {
        "table": {
          "table_name": "a",
          "access_type": "index",
          "key": "id_path",
          "key_length": "767",
          "used_key_parts": ["id_path"],
          "loops": 1,
          "rows": 271,
          "cost": 0.060074355,
          "filtered": 100,
          "attached_condition": "a.id_path like <cache>(concat('313','/%'))",
          "using_index": true
        }
      }
    ]
  }
}

Result

category_id
357
574
575
576
577
578
359
579
580
581
361
587
588
589
590
591
363
592
593
594
595
596
571
582
583
584
585
586
572
597
598
599
600
601
573