Our users have been seeing the same issue on the production release of iOS 16. The restart workaround mentioned by WJohn does work (and we are now instructing users to restart their phones), but this definitely feels like a big miss and something that should be fixed.
However the bigger problem remains -- two iOS versions later and Apple still has not given developers a way to properly trigger the local networking permission programmatically or check it's status programmatically with a sane API and not needing to resort to these sorts of workarounds.