Great news, the problem seems to be resolved in iOS 14.1 (18A8395).
We did multiple tests and every time the app is launched after a re-install, the Local Network permission is shown in the app.
Also the Local Network toggle is present in Settings App -> Privacy -> Local Network.
Added bonus
Finally it's possible to consistently reshow the Local Network permission - https://developer.apple.com/forums/thread/663839 in the app without uninstalling it first, by going to Settings App -> General -> Reset -> Reset Location & Privacy
Thanks Apple for resolving this.
Topic:
App & System Services
SubTopic:
Core OS
Tags: