Postgres how to update first row in the child table for all parent entries
Possible question interpretation:
UPDATE workflow_task
SET task_Type = CASE WHEN workflow_task.id = first_row.id
                     THEN 'POC'
                     ELSE 'Appr'
                     END
FROM ( SELECT MIN(id) id, workflow_id
       FROM workflow_task
       GROUP BY workflow_id ) first_row
WHERE workflow_task.workflow_id = first_row.workflow_id;

https://dbfiddle.uk/?rdbms=postgres_12&amp;fiddle=08c60035f735ae557100dde8a7623008
workflow table not needed for this operation.