We are working to improve interoperability. Will keep you posted as this is enhanced.
As I know, PowerBI within PowerApps can refresh automatically but with a PAID PLAN.
A free PowerBI needs manual refresh.
I have read thru and tested before.
What is the status of this improvement?
As of earlier this year, this control now supports Reset, and has an additional property for controlling when it loads and unloads its content (LoadPowerBIContent).
Support for filtering is still under review.
I hope this helps.