Maybe a lot of time hadn't passed between when Loki and Sylvie had confronted He Who Remains, it was hard to say when Mobius spent the majority of his time within the TVA and as they all knew time worked differently there. However much time had passed though, between there and here - there was plenty to filly Sylvie in on, things best conveyed in person rather than through messages.
And it was clear she had things here that she was interested in showing him. So Mobius decided meeting with her was the best thing for it. She could show off for him, and he could explain the way things had gone, and maybe at the end of it all they'd come out of it both feeling - well he didn't really know. He was still processing what he felt about all of this and so if nothing else maybe talking with Sylvie would help him sort that out.
So Mobius made his way outside, seeking out the little home that had apparently been made for Logator, of course there would be more than one Loki here, Mobius was beginning to suspect there could be no place in existence on any timeline with just one.