Some changes in the implementation of what used to be kde-apps.org several years ago went past me and I neglected to update Tellico with the changes. Prompted by a Tellico user sharing a new entry template with me, I went back to figure out what was going on.
Tellico knows where to look for new user templates by checking the options in the tellico-template.knscrc file. If you add the changes from a recent commit to the .knscrc file, you should be able to run Tellico and then once again, select new templates to download.
The templates are also available directly from store.kde.org. The recent one I uploaded, with permission from the user, is called ZAP Group Narrow. Within Tellico, the download dialog shows a description of the template along with a button the install it locally.
The fix for the download location itself will be included in Tellico version 3.4.