"The Great Work" shows that the Emperor had a hand in setting up Cawl for the Primaris project. He spoke to one of the people who's memories Cawl would eventually acquire, knowing that Cawl would eventually remember the conversation.
Having said that, I tend to agree that FOM is referring to the GKs.
Oh, he definitely interacted with Cawl (but tbh that's more of a function of just how many specialists Cawl gobbled up and how those were the same people the Emperor had worked with) , but the entire project was never his brainchild, as it were. Even when he spoke to Cawl, he was very non-specific in the discussion.
The Emperor had already made his move in response to chaos already in the GK.