I figured out the problem. I now understand that Zen Cart also needs to have the admin translated and not only the store front end. So basically, I faked a translation in the admin/languages (unsure about the path, though) by copying english.php and english/ and renaming the to swedish.php and swedish.php. I believe I also modified the admin settings file so that it uses proper swedish langauge settings.

Maybe this is obvious for seasoned Zen Cart devs, but I haven't read any documentation, but only solved my problems using trial and error. I still haven't grasped all of the dependencies and the general architecture of Zen Cart, but it is nevertheless promising.