Indeed the left part of the brand filters seems to have been "disconnected". You just have to import the right categories and put the right links generated in the left part.
Or possibly use the widget provided by the module to display them dynamically.
(However, given the design with the small pictograms, I think the easiest solution is to place them by hand).
In short, there is surely 1 hour of work to reconnect the good links now that you have the content.
For research, the functionality was available in the module.
Ex: brand / search? s = topo
So just put this link in the search field. With this information new developers will be able to get by much more easily indeed.
At worst, to see how the native works, the best is to put the native theme of magento back temporarily to fully understand.
Category: IT & Programming