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Which settlement did you assign him to lead? Was it Sanctuary?
Codsworth is problematic in any game, including the vanilla game. And I think he is worth more detailed study. What and when he will do things seems tied to certain quest progressions.
I would suggest trying to make him the leader at RR. Go to RR by yourself and assign him to lead via the desk. Wait. Maybe even sleep for twenty four hours. I know I have got him to RR this way before. I can't remember right now if it was a Conqueror run after killing Preston or a regular SS run where I left Preston in the Museum. I almost never let him leave the museum.