I'm pretty sure the AT being able to see the future is correct; otherwise, how would Grisha be able to interact with Eren's "ghost" in these chapters? It's even more clear this chapter when he suddenly is able to see Zeke, and we get a shot of Eren standing right behind Grisha, implying that what Grisha keeps seeing is Eren's POV of his own memories. So he must have been able to see the future, as he said.
The timeloop aspect comes in when Eren, by being a "ghost" inside a memory (rather than just switching POVs as it usually happens when shifters see memories), is able to use this future-seeing ability to interact with Grisha through his own memories. Hence why he thanks Zeke for "opening up this path" by taking him inside Grisha's memories.