Updated implementation, based on B4XPages of https://www.b4x.com/android/forum/threads/android-bluetooth-bluetoothadmin-tutorial.14768/#content. The code is much simpler compared to the previous example. Note that you can call Serial.Listen without making the device discoverable. This is useful...
Dont worry, BluetoothAdmin does work on Android 13 - I am using it myself right now. I would like to help you more but I have no idea of what you are trying to accomplish. The Bluetooth chat example is a useful example but it illustrates a specific mode of communication - in this case between two 'phones. It might not be exactly what you want to do. Different types of application can require different permissions, by the way.
That is not likely to be the problem - I do not use B4XPages either as a rule, and never yet with Bluetooth. And the permissions that you need will be in the RuntimePermissions library, I am sure.
In my case I am communicating with a microprocessor via an HC-05 Bluetooth module. In that case only these two permissions are needed and everything is fine ...