
The newly added action in Power Automate desktop can have custom message of the flow run where are those messages stored locally.
They are not stored locally. They are pushed to the flow run action details in the cloud portal. When you have a Premium license, you can see your desktop flow runs in the cloud portal here:
And when you open one, you can see all of your actions logged there, like this:
If you add a Log message action, the custom message will also be logged there. That's the only place where it is actually stored/logged.
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