You can use the Merge statement to update on a target table from a source table.
Refer: https://learn.microsoft.com/en-us/sql/t-sql/statements/merge-transact-sql?view=sql-server-ver16
In your case, try the below statement
MERGE Table1 AS TARGET
USING Table1 AS SOURCE
ON (TARGET.ID= SOURCE.ID)
WHEN MATCHED
THEN UPDATE SET TARGET.COLA= SOURCE.COLB;
Also be noted that some times, you might need to have some other conditions to be matched before doing the update, In such cases you can add condition after When Matched Clause. See the example.
MERGE Table1 AS TARGET
USING Table1 AS SOURCE
ON (TARGET.ID= SOURCE.ID)
WHEN MATCHED and Target.ID <>2 --you can add as many conditions here with Target and Source
THEN UPDATE SET TARGET.COLA= SOURCE.COLB;
Hope this helps