Power Automate Dataset Refresh, Last Refresh Date

In this where the last refresh date time stamp does not update when using the Power Automate Button, is expected, when you use the refresh option within pbi desktop, it updates the date time. LocalNow() value because it's running within the context pf pbi desktop. When you are trigger a refresh using Power Automate or any other external method, it wont update the datetime.LocalNow() value in PBI report because the report and the refresh process are separate.

Use a data source timestamp, the load the timestamp into your model and after that display the timestamp in your report.

In Power Query go to Home after that Manage Queries after that New Source and Blank query and in the formula bar add DAX in which create a calculated table with the "Last Refreshed" timestamp.

let
Source = #table({"Last Refreshed"}, {{DateTime.LocalNow()}})
in
Source

Click on done to create the query, and then load it into ypur data model. In your report, use a card visual to display the "Last Refreshed" timestamp from the calculated table.