Looking this up, I don’t think it’s actually group related. Instead, xfce seems to use polkit policies to allow the user to execute this file. Search results for “xfpm-power-backlight-helper authentication needed” seem to suggest improper installation.

If you’ve installed it through nix, I’d try older version, or stable if you’re on unstable, etc. Though I myself don’t sue xfce, so I don’t actually know.