Grouping item recursively in sql

I have this table (test.mytable in the sql script below)

CREATE OR REPLACE test.mytable (item STRING(1), I_groupe STRING(1));


INSERT INTO test.mytable (item, I_groupe)
values
('A', '1'),
('B', '1'),
('B', '2'),
('C', '2'),
('D', '3'),

My purpose is to group the item together. My expected result is :

I would like to group the item A and B because they have at least one Intermediate_group in common (Intermediate_group 1). Then I would like to group A,B with C because there is an Intermediate_group in common (Intermediate_group 2). Item D has no intermediate group in common with other items. It is therefore alone in its final group.

I have this code:

  WITH TEMP1 AS (
  SELECT *
FROM (
  select item as item_1,
             array_agg(distinct I_groupe) as I_groupe1
      from test.mytable
      group by item_1) AS AA
   cross join
     (select item as item_2,
             array_agg(distinct I_groupe) as I_groupe2
      from test.mytable
      group by item_2
) AS BB
)
,
 
TEMP2 AS (
SELECT item_1, item_2,
  ARRAY(SELECT * FROM TEMP.I_groupe1
    INTERSECT DISTINCT
    (SELECT  * FROM TEMP.I_groupe2)
  ) AS result
FROM TEMP1
)
,

TEMP3 AS (
SELECT item_1, item_2, test 
FROM TEMP2, unnest(result) as test
)
,

TEMP4 AS (
SELECT STRING_AGG(DISTINCT item_2) as item, STRING_AGG(CAST(test AS STRING)) as I_groupe
FROM TEMP3 
GROUP BY item_1
)
,
TEMP5 AS (
SELECT item, I_groupe
FROM TEMP4, UNNEST(SPLIT(item)) as item, UNNEST(SPLIT(I_groupe)) as I_groupe
)

I repeat this code/process manually three times for this "toy" example and finish by a select distinct to get only one row by Final_group

SELECT DISTINCT *
FROM TEMP14

But in a real example it's not scalable. I would like to use a recursive function or a loop to automate this code.

Thanks in advance for your help