Group Jive bases on the Kunena Engine
No idea where you got this information from, but it's not correct. GJ is not based on anything of Kunena.
posting a URL in Kunena automatically produces a link. Why does this not work in GJ?
Because GJ does not do that. You need to supply the HTML. There is no such content parsing.
When I use the WISIWIG then I can transform the intended link into a link using the link button... Am I being stupid or have I missed a setting? I have set it to enable content plugins (or disable... same result)
You need to use the link button in the WYSIWYG editor or supply the HTML for a link. It's working as designed. It does not have auto content parsing into links or anything of the sort, that would be a feature of your WYSIWYG editor if available.