It is possible the wallet you are using does not support LNURL Auth.
A list of wallets that do: Alby Balance of Satoshis Blixt Breez Blue Wallet Coinos LNBits LNtxtbot Phoenix Simple Bitcoin Wallet Sparrow Wallet ThunderHub Zap Desktop Zeus
The generated URL contains nothing private. It is basically just the domain of the service, for example stackernews with a few url parameters that define if its for logging in or signing up and then a random 32 byte string. The QR code just makes it easy to transmit between devices but services will also provide an encoded LNURL string.
The wallet will sign that random string and submit it back to the service to authenticate.
So for a wallet to support LNURL it must
  • decode LNURL strings
  • sign the random 32 bytes of data
  • submit to the service to authenticate with that signature.