Well I'm running the latest iOS 13.1 on my XS and so far every app, even ones that haven't been updated specifically for ios13 are working...
Developers can update their apps to work with iOS 13.x, but they have to use the SDK from the currently released version of iOS... they can be creative with work-arounds, etc... and not every API call is changed with each new release... so many of the apps will continue to work on the beta releases with minor issues or no issues at all. It all depends on what the app is doing, what APIs it's using and what Apple has done to modify or deprecate those API calls.
I can guarantee you that none of those apps are using the iOS 13.x SDK... Apple will not approve them for release until iOS 13.x is released.