Ishterebinth was outsmarted the moment they let Sorweel inside their mansion, I think. Sorweel is, in some fashion, similar to Psatma in that they are a form of Oracle, though the mechanism is different. The Torturer's reaction is just the most profound because his sins are so extreme; millenia of sadism and horror supposedly hidden, only to be found by the Gods and damned anyway. This is also true to some degree for whoever else was "seen" by Sorweel, before they realized their mistake and slapped the Amiolas on him. By which time they were already God-Entangled (and always were because the Gods exist in the eternal Outside).
Note that at least two birds are mentioned during this section, specifically after Sorweel gets the Amiolas: one is trapped in the chutes where where he first wakes up, and then later during his descent with Lastborn on the Haul, into the Holy Deep where the boatman, the Most Ancient Warrior, is singing songs and tossing pork. As the Haul is being lowered, a bird (implied to be a Stork, a.k.a. Yatwer's favorite spy). So, either Yatwer got desperate when Sorweel's perspective was fucked with by the Amiolas and sent in the birds to compensate OR the birds (having had literally thousands and thousands of years to get in there) have long since spotted the Nonmen and the Amiolas was just a way for Kellhus to get Yatwer's blessed face off of Sorweel when Oirunas "rips him in half", I.E. removing the Amiolas (Kellhus "killing two birds with one stone?). Seemingly, the blessing from Porsparian that put Yatwer's loving "face" over Sorweel's was also removed. This lines up with how Serwa perceives him as a warrior when he and Oirunas finally crash the party/gangrape going on upstairs.
I'm not sure how to parse the difference between the metaphysical connections to a God regarding characters like Sorweel, Porsparian, Psatma, and the White-Luck Warrior. I think Psatma's seemingly exponential growth in power (mainly after the reward of youth and foresight after lifelong sacrifice) is akin to Cnaiur's partial transformation into a Ciphrang despite still being a live. Cnaiur, much like Psatma, spend their entire lives devoted to their respective -- and interestingly, opposite -- deities, those being Yatwer (Birth/Life/Creation) and Gilgaol (War/Death/Destruction).