MySQL recurssion heirarchy

Question

** Is there any way that I can visualize the steps of recursive CET in mysql (Something probably similar to https://pythontutor.com/

I am trying to understand the order of execution for the recursive CET Part of my query, I am reaching the intended output anyway which is counting the total family members per each member having null parent

Schema (MySQL v8.0)

CREATE TABLE Family (
  person INTEGER not null  PRIMARY KEY,
  name VARCHAR(255) NOT NULL, 
  parent INTEGER
  )
 
 ;


INSERT INTO Family (person, name, parent) VALUES 
                     (1,'Sabri',NULL),
                     (2, 'Reo',1),
                     (3, 'Fadaa',1),
                     (4, 'Sahar',1),        
                     (5, 'Helen',3),
                     (6, 'Mimi', 3),   
                     (7, 'Reo',1),
                     (8, 'Micheal',Null),
                     (9, 'Antoni',8),       
                     (10, 'Selen',9);

---

Query #1

WITH RECURSIVE cte as 
(
  SELECT person, person as root_id, parent
  FROM Family
  UNION ALL
  SELECT cte.person, Family.person,  Family.parent as parent
  FROM Family
  JOIN cte ON cte.parent = Family.person 
),





Agg_data as 
(
  SELECT  *  FROM cte
  ORDER BY person
),


Top_members as 
(
  Select Person, root_id
  FROM Agg_data  where parent is null
)

Select distinct root_id as Top_parents,
count(Distinct if( root_id !=person, person, NULL)) AS members_Count

from Top_members
group by 1;

Output

Top_parents	members_Count
1	6
8	2

---

View on DB Fiddle

However I am Interested in understanding the order of recursion execution for the output below

Like iteration 1 output is ? iteration 2 output is ? iteration 3 output is ? and so on

select * from cte, this is the output

person	root_id	parent
1	1
2	2	1
3	3	1
4	4	1
5	5	3
6	6	3
7	7	1
8	8
9	9	8
10	10	9
2	1
3	1
4	1
5	3	1
6	3	1
7	1
9	8
10	9	8
5	1
6	1
10	8

---