ok a lot wrong with this sentence, firstly drunkenslug is not a newsgroup, its a usenet indexer, indexing content posted to usenet and turning indexed binaries into nzb files that you then download, secondly nzbget is an application not a 'newsgroup', so yeah confusion abounds here.
why are you trying to connect to drunkenslug using port 563?, i would assume you would be connecting to it via HTTPS, so port 443 or port 80 if HTTP.
If you want to automate downloads then use something like sonarr for tv or radarr for movies and point that at drunkenslug, or better yet use prowlarr and let it handle this side of things for you.
If you aren't fussed about automation then simply go to drunkenslug using your web browser, login, search and download the nzb file and upload to sabnzbd via the sabnzbd web ui.