Years of use in the environment of a firearm, that can vary drastically on how the owner uses and cleans it, it would NOT be surprising to find all the grease gone, or the grease still there. In cars, in my experience, even when you can't see any grease there anymore, whether some is there are not, it did its job preventing corrosion and seizing far better than putting things together dry.
I say do what the TM says, I can't remember what that is, if the TM is silent on the issue, then I would put a thin film of grease on the extension, it would NOT hurt and could help.
Anti-Seize would work, might even do better, just consider NOT mixing anti-seize with grease on the barrel nut threads. Mixing lubes can give unexpected results, like they are incompatible and will break each other down, leaving you with less protection. Pick one or the other for the threads and don't mix the lubes together.