Yeah, it sounds like you basically extracted a new installation within the existing folder. Delete that new folder and pay attention to what you're extracting and to where.
What you really want to do is select the contents of the Headmaster folder in the ZIP, and extract it to the existing main Headmaster folder (there should be game, lib, & renpy folders and four other files. These will overwrite the existing ones).
(I’d suggest renaming the Headmaster folder, just for your own reference because it's not going to be version 12.3.1 any more, but that's up to you.)