SELECT 
  pc.product_id 
FROM 
  cscart_products_categories AS pc 
WHERE 
  pc.category_id IN (
    SELECT 
      c.category_id 
    FROM 
      cscart_categories AS c 
      LEFT JOIN cscart_products AS p ON p.product_id = pc.product_id 
    WHERE 
      c.parent_id = 564 
      AND p.status = 'A'
  )

Query time 0.01303

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "1020.28"
    },
    "nested_loop": [
      {
        "table": {
          "table_name": "c",
          "access_type": "ref",
          "possible_keys": [
            "PRIMARY",
            "parent",
            "p_category_id"
          ],
          "key": "parent",
          "used_key_parts": [
            "parent_id"
          ],
          "key_length": "3",
          "ref": [
            "const"
          ],
          "rows_examined_per_scan": 22,
          "rows_produced_per_join": 22,
          "filtered": "100.00",
          "using_index": true,
          "cost_info": {
            "read_cost": "0.25",
            "eval_cost": "2.20",
            "prefix_cost": "2.45",
            "data_read_per_join": "239K"
          },
          "used_columns": [
            "category_id",
            "parent_id"
          ]
        }
      },
      {
        "table": {
          "table_name": "pc",
          "access_type": "ref",
          "possible_keys": [
            "PRIMARY",
            "pt",
            "idx_pc_product_id_type"
          ],
          "key": "PRIMARY",
          "used_key_parts": [
            "category_id"
          ],
          "key_length": "3",
          "ref": [
            "dev2.c.category_id"
          ],
          "rows_examined_per_scan": 101,
          "rows_produced_per_join": 2236,
          "filtered": "100.00",
          "using_index": true,
          "cost_info": {
            "read_cost": "11.29",
            "eval_cost": "223.67",
            "prefix_cost": "237.42",
            "data_read_per_join": "34K"
          },
          "used_columns": [
            "product_id",
            "category_id"
          ]
        }
      },
      {
        "table": {
          "table_name": "p",
          "access_type": "eq_ref",
          "possible_keys": [
            "PRIMARY",
            "status",
            "cscart_products_product_id_index",
            "idx_status"
          ],
          "key": "PRIMARY",
          "used_key_parts": [
            "product_id"
          ],
          "key_length": "3",
          "ref": [
            "dev2.pc.product_id"
          ],
          "rows_examined_per_scan": 1,
          "rows_produced_per_join": 1615,
          "filtered": "72.23",
          "cost_info": {
            "read_cost": "559.19",
            "eval_cost": "161.55",
            "prefix_cost": "1020.28",
            "data_read_per_join": "11M"
          },
          "used_columns": [
            "product_id",
            "status"
          ],
          "attached_condition": "(`dev2`.`p`.`status` = 'A')"
        }
      }
    ]
  }
}