i think background app refresh just doesn't work in the betas. not on my phone, neither on my watch. mostly.
it works sometimes but for the most part it refuses. my watch complications have refused to update the weather display and just show -- instead of the current temp/UVI. even entering the weather app does not help.
as for ios, the podcast app only updates the widgets upon entering it. weather app only will update the weather widget for a limited amount of time, after which it will just say "weather unavailable" where you must reenter the weather app to make it work again. it works just fine on iOS 15! source: iPhod! all widgets there update just fine!
tim cook why must you do this to me