I'm not sure what "mod menu" means regarding Fallout 4, but if you mean the Creation Club stuff, the Gog version does not include the Creation Club. I'm pretty sure this was disclosed on the store page though, so I guess that isn't what you're talking about. But I've been playing Fallout 4 since it was released and I've never encountered a "mod menu" so the Creation Club thing is the only thing I can think of that is mod related. Creation Club content is basically mods.. but mods that you must pay in order to use.
EDIT: Screenshot showing the Creation Club content from the Store Page.
Please note that the DRM-Free version of Fallout 4 GOTY does not include the Creation Club feature. For a premium modding experience, we recommend Nexus Mods, which provides free access to tens of thousands of amazing modifications, and hundreds of curated collections.
