First install the NixOS module for the server components of smos. Then activate the api server as follows:

{
  services.smos.production {
    enable = true;
    web-server = {
      enable = true;
      log-level = "Warn";
      hosts = [ "smos.example.com" ];
      port = 8403;
      docs-url = "https://${builtins.head config.services.smos.production.docs-site.hosts}";
      api-url = "https://${builtins.head config.services.smos.production.api-server.hosts}";
    };
  };
}

See also the reference documentation for this nixos module.