However, I am really lost, should I add the zotero package in the home manager, what tells nixos rebuild to install zotero, etc…
I am not really explaining my problem super well, since I do not think I understood how overlays work (I understood they are used to change packages, but besides that…).
The main idea of overlays is that it allows adding or changing attributes(packages) in pkgs. In this case when something in your config would pull in pkgs.zotero – the overridden version will be installed.
To have this version installed – you can add environment.systemPackages = [ pkgs.zotero ]; somewhere in your configuration.
Are you using home-manager as a module or running it standalone? Looks like module, since not seeing the home-manager part of the flake, but just to make sure.
I was thinking, maybe I have to add the overlays to the NIX_PATH as written in the wiki (Overlays - NixOS Wiki).
On the system level
If you want your overlays to be accessible by nix tools and also in the system-wide configuration, add nixpkgs-overlays to your NIX_PATH:
NIX_PATH="$NIX_PATH:nixpkgs-overlays=/etc/nixos/overlays"
because in /etc/nixos/overlays, I indeed see the added zotero overlay.