Hi JP,
Yes, you can do this,
You can use Error Handling for the same,
Right-click on the Rest Service activity, and choose set error handling,
Now choose custom without rollback,
Now you will see a yellow circle in your Rest activity,
From this yellow circle, you can make another flow, which will be activated when there’s an error,
And you can customize it in whatever way you like,
for ex:
Now you can show a message, using show message and show a log message with the latest error as the message string,
Let me know if you have any issues,
Hope it helps!!