I encountered the same problem, and after much searching I think Paizo does not give us any details about the church of Pharasma in Caliphas or in Ustalav beyond that is the predominant religion.
Based on the culture and society of Ustalav, I believe the Church of Pharasma is well established and organized but not as well hierarchical and centralized. Each priest, cleric, monk and minister is responsible for its own shrine, monastery, temple or church responding very sporadically to the bishop of the county or region, and the hierarchy between churches depends on the size of the population they serve.
30 years ago Caliphas become the capital of Ustalav and since then the temple of Pharasma here seen their power and influence grow, seeing itself as the logical center of the faith, something that many are in disagreement, especially the traditionalist and bitter church of Ardeal and the increasingly intransigent fundamentalist church of Barstoi. These differences have not yet caused a major division within Pharasma church where most of its clergy clinging to the provincial traditionalism characteristic of Ustalav. Still Maiden's Choir has become one of the most dynamic, powerful and ambitious churches but also indulgent and arrogant immersed in the political intrigue that shake the Principality and its capital.
The church of Pharasma in Caliphas is completely ignorant of the vampire society that infest the city , vampires have dedicate centuries maintaining their presence secret. Nor they think the Whispering Way a too dangerous threat, thinking they are a cabal of decadent necromancer who clings to their old reputation, who have no real power anymore. The church is also very concerned to maintain Pharasma religious hegemony in Ustalav so they dislike the presence or intervention of clerics or representatives of other gods.
If the players turn in the Raven's Head is possible that the church believes it was his sacred duty to return it and do not give them any reward. That would create tension between the players and Pharasma church so they would not go to them when they encounter the vampires. You could even make them believe that vampires have infiltrated and corrupted the church. (Note the name I gave to the high priest of death)
Maiden's Choir:
Archbishop/Mother Verith Thestia (N female cleric 12) head of the temple and high priest of birth
Bishop Longinus Lancea (NE male cleric 14) high priest of death
Bishop Ruslana Toader (CN female cleric 10) high priest of prophecy
Zetiah Mardhalas (LN female inquisitor 6) high exorcist
