Privileged Helper Registration

History
Prior to macOS Ventura privileged helper tools were registered through the SMJobBless api and installed into the the global /Library directory. With the advent of macOS Ventura this api was deprecated by Apple and the recommended replacement is the SMAppService api. This new api has the advantage that the helper tool is not copied to the global directory but is instead invoked directly from the main application bundle and will be in sync with its associated application.

The SMJobBless api is tricky to set up and there are a number of "gotcha" holes to fall through, leading to a non working helper.
And to repeat myself:
The SMAppService api is tricky to set up and there are a number of "gotcha" holes to fall through, leading to a non working helper.

Expected Behaviour

When all goes well, on starting the application checks to see if the helper has been registered and is enabled in the Login Items & Extensions panel of System Settings. When these conditions are met, the helper tool is started and the application goes about its normal duties.

Should the application not be either registered or enabled it opens Login Items & Extensions panel of System Settings and then displays an alert waiting for you (the user) to enable the application. Your password will be required.

You MUST do this for the helper tool to be able to run. When you enable the setting, the application alert will close and hopefully the privileged helper will start.

Sometimes macOS is unable to start the helper (reasons unknown to me) and in this case another alert will be presented. One of the options in the alert dialog is to restart the application. Please try this option first.

What Could Possibly Go Wrong?

ProblemWork-around
The password field in the settings authentication dialog will not accept your password. Quit/Force Quit the application if it is running. Close Systems Settings/Login Items & Extensions and try again.
All looks good in System Settings but the helper tool has not started. Quit/Force Quit the application if it is running. Close Systems Settings/Login Items & Extensions and try again.
All looks good in System Settings but the helper tool has not started. Move the application to a different folder but do not run it. Open and then close Systems Settings/Login Items & Extensions. Move the application to your preferred folder and try again.
I moved the application to a different folder and now it wont run. Quit/Force Quit the application if it is running. Close Systems Settings and try again.

As you can see, problems may be sorted out by succesive retrys.

Failing this then you can try logging out and trying again after logging back in.

If it is still failing, then reboot and - yep - try again.

This is less than ideal but hopefully Apple will eventually make this registration process a bit more reliable.
Mike Bombich (Carbon Copy Cloner) has a very good article at his web site about these problems with the installation of the helper tool for Carbon Copy Cloner: CCC FAQ