Still, I can not access the response. Am I doing something wrong? I would like to use {{ !update_item.data.success }} as 'Only run when' and {{ !update_item.data.message }} as description.
It seems the response is not available on failure. Data should not be null, I see the response behind the popup. Am I missing something?
The failure handler shouldn't run no matter what unless the query itself fails. You should be able to set the failure condition in the "Response" settings as you had it by referencing {{ data }} instead of {{ update_item.data }} (see the docs @ScottR linked for reference):
Otherwise, you can add two separate 'Success' handlers that run under different conditions (one for a true success and the other for a success that should be seen as a failure):