I think these "7 singleplayer reward" skins have always been a bit buggy. These skins are only visible on the soldiers customization screen. Why aren't they on the inventory screen?
I got the "His Lordship" skin for C96 a few years ago, I still have it.
my screenshot with customization screen:
I don't think you understand . . . I haven't completed the codex entry. The codex has not registered as being completed. I do not have the codex challenge required to unlock the skin, despite completing the objective.
