For Nagios XI is usual web access URL httphttps://some.domain:port/nagiosxi
In that case, For Nagios Core is usual web access URL is httphttps://some.domain:port/nagios and that address should be used in Nagios API URL configuration field.
To check if the URL is correct, try in the web browser access http://some.domain:port/nagios/cgi-bin/objectjson.cgi?query=hostgrouplist
some.domain and port should be replaced by actual values from your installation
The actual value should replace some.domain for your Nagios installation.
The extension uses Basic authentication for Nagios JSON API, the Digest authentication is not supported by the extension.