I have not duplicated this problem, Martin. I downloaded a brand new oXygen on a virgin Lubuntu system yesterday, and have not installed any add-ons nor plugins. It has the exptected array of templates like TEI all, TEI Tite, TEI P4 (deprecated), etc. when I issue CTL-N to create a new file. (I don't know what you mean by File / New / Framework Templates.)
I just updated my Oxygen to the latest release, and I can't see any TEI P5 templates other than the JTEI template. This is an install which doesn't have the bleeding-edge version of the plugin installed. In the Framework folder I see all the relevant files, but I don't see anything other than JTEI when I go to File / New / Framework Templates. Can anyone else who's got the latest Oxygen check what you see?