Hi Jay, thank you for your comment.
The notification really depends on your application. Are you use Power Apps?
Checking if a refresh is already running might also be possible come to think of it. You could create a second TimeStamp table and make sure it runs at the start of the refresh (by referencing it in the other tables). That way, you can check if that timestamp changes and if it does it means the refresh has started.
This is just an idea that I have not tested, but I do not see why it wouldn't work.
Good luck!