Complex recursive query postgreSQL - postgresql

Question

I have a table agent with an id and parent id. This is an adjacency list.
Each agent can sponsor multiple agents.
ID
sponsorId
1
null
2
1
3
2
4
1
5
3
I want to keep the query with a maximum of 4 level of depth.
I already build a recursive like this to get children per level for a specific user, here is the query
WITH RECURSIVE subordinates(id, sponsorId, LEVEL) AS(
SELECT "id","sponsorId",0 AS LEVEL
FROM "Agent" AS t
WHERE id = 1
UNION ALL
SELECT e."id", e."sponsorId", s."level" + 1 AS leve
FROM "Agent" AS e
INNER JOIN subordinates s ON s."id" = e."sponsorId"
WHERE LEVEL < 4 )
SELECT s."level", array_agg(id ORDER BY s."level") AS childrens
FROM subordinates AS s
GROUP BY s."level";
This query give an array of ids per level for a specific user:
ID
sponsorId
0
[1]
1
[2, 4]
2
[3]
3
[5]
4
[]
But I also want the list of all user with a column per level and a total column, like this but I can't get to make this working, like in this table
ID
level1
level2
level 3
level 4
1
[2, 4]
[3]
[5]
[]
2
[3]
[]
[]
[]
3
[5]
[]
[]
[]
4
[]
[]
[]
[]
5
[]
[]
[]
[]
Could you help me writing this query ? I have only small experience with recursive query?
I try a lot of different things to make it works but I don't get how I can create a specific column a bundle the result of the recursive iteration on this new column.
I did manage to get children array for a specific user but the result I get is "vertical", I would like to get it like it the example table above.
I guess I can maybe find something like PIVOT to achieve that, but I never used it so I don't really know how to handle that.