So, there is no way to make that action Synchronous, which means you would have to do something like
1) in power bi, log any refresh events somewhere like SharePoint, then you would have a flow that triggers when the Refresh completes (whether successful or not) and then you would send your notification
2) Track using power BI Alerts that can be sent out, preferably some DAX so that when its complete it can do the notification
Also remember that if you tell it to do a refresh, but one is already going, this refresh will NOT trigger anything so you may not get anything back ever and be confused, that of course plus refresh limits in a day (depending on your license).
3) You can create a Do Until that then leverages the HTTP Action to check the power Bi Rest API Endpoints, checking the Refresh History / Refresh Execution Details to see if it worked or not and then do your notification. although this would potentially make this long running (depending on your refresh or state of), plus if it didn't actually trigger it because one is already running, you'd have to tak that into account so you do not try to Do until forrever (ok it would not be forever, as you would have a time out).
Those are the only ways I can really think of based on your ask, since it won't block :-( I am afraid.
If these suggestions help resolve your issue, Please consider Marking the answer as such and also maybe a like.
Thank you!
Sincerely, Michael Gernaey
