How can I troubleshoot this re-occuring prompt to give a mysterious app security access?
This may be caused by extensions that were installed when the Eltima USB Networks Gate for Mac application was installed.
A couple of possible solutions I found:
This one from an Eltima forum which it's recommended to run in safe mode:
sudo /Library/Frameworks/EveUSB.framework/Support/uninstall

The other is from a Stack Overflow post that provides a script for finding and removing any Eltima USB Networks Gate for Mac extensions.