Mac OS 13.7.8, newest version of FontBase, internet connection is (obviously) active. After installing the app there was nothing in the Google folder. Trying to drag a google font downloaded from google into that folder results in the fontmarket folder turning green instead. I do have a firewall but it doesn’t show that anything related to fontbase was denied.
EDIT: It was my firewall after all. Although there were no requests for fontbase to contact google servers initially, when I turned off my firewall and restarted fontbase, the google fonts appeared. When I re-enabled the firewall, there were numerous requests from fontbase to contact various servers, one of which was fonts.gstatic.com (which I allowed permanently). I think I’m good.