First I would recommend using a multiline f-string in spark.sql like this...

spark.sql(f'''
    insert into default.batch_run 
        (
        task_name, 
        start, 
        end, 
        status
        ) values (
        {param_task_name},
        {param_start},
        NULL,
        {param_status}
    ''')

There are other options I havent tried if NULL doesnt work like

None

or

lit(None)

Let me know which works for you 🙂