Reading the announcement it seems this feature is ready.

I've installed the beta version 5.1.4  from Play Store and while the UI is clearly there it's completely non-functional. At the start of the app I can briefly see the following notification:
"Brainzplayer requires local storage permissions to play local songs"

However there never is a dialog asking for permission.

Device: Pixel 6 Pro
Android: 13 (TP1A.220905.004)