Optimize update query which uses MAX()

This is question is for Oracle 19 DB.
I need some help optimizing this update statement:

UPDATE T1 T1
   SET T1.COL1 = (SELECT MAX(T2.COL1)
                   FROM T2 T2
                   WHERE T2.COL2 = T1.COL2)
 WHERE T1.COL2 BETWEEN :1 AND :2
   AND T1.COL1 IS NULL
   AND EXISTS
 (SELECT 1
          FROM (SELECT MAX(T2.COL1) 
                  FROM T2 T2
                 WHERE T2.COL2 = T1.COL2) V1
         WHERE V1.COL1 IS NOT NULL)

I like this answer:

https://stackoverflow.com/questions/65829430/massive-update-vs-merge-performance-on-oracle

and I tried doing similar but my problem is that my update has MAX() and I don't know how to optimize it.

Merge, as you said:

merge into t1 
  using (select t2.col2, 
                max(t2.col1) max_col1
         from t2
         group by t2.col2
         having max(t2.col1) is not null
        ) x
  on (t1.col2 = x.col2)
  when matched then update set
    t1.col1 = x.max_col1
  where t1.col2 between :1 and :2
    and t1.col1 is null; 

Use a MERGE statement with a HAVING clause to perform the V1.COL1 IS NOT NULL filter (or, alternatively, a WHERE clause before the GROUP BY):

MERGE INTO T1
USING (
  SELECT col2,
         MAX(col1) AS col1
  FROM   t2
  -- WHERE col1 IS NOT NULL
  GROUP BY col2
  HAVING MAX(col1) IS NOT NULL
) t2
ON (t1.col2 = t2.col2)
WHEN MATCHED THEN
  SET   T1.COL1 = t2.col2
  WHERE T1.COL2 BETWEEN :1 AND :2
  AND   T1.COL1 IS NULL;