I am suggesting the addition of an IsAsynchronous parameter (non-mandatory, set to False by default) on the Refresh Data UI Flow Screen action, to tell the Refresh Data block to run the given Data Source in either an asynchronous or synchronous way, depending on the value of that input.

This will spare the work of creating dedicated screen actions to refresh the Data Sources separately in a Screen Action to conceive a pure asynchronous Data Source Refresh, when applicable.

Best regards!