Leareth got what he came for.
He continues his research. He can triangulate his search much better, now, since he has a lot more data on the world where Kib - is from, or grew up in, it's not clear but it doesn't seem like he was born the usual human way. In fact, the Healers have mentioned to him that he...doesn't have a belly button?
He's confused, but his confusion about the world that Kib called 'Stork' isn't the highest priority here. Their 'servantmaking' magic is strategically relevant but mostly he needs to find a way to travel to Arda at all, before it's too late.
Leareth is still baffled about the whole memory insertion dreams thing, but loath to re-enter his traumatized prisoner's room to learn more.
He's making faster progress, though. At this point it's almost certainly a project of months or years, not decades.