How powerful are the Elementals post-Calamity?

[Cleretic]

Belief in a deity does make it easier to concentrate Faith, certainly, but it's not required that the target be believed to be a god or similar for Faith to influence them, only that there be enough belief in a thing to pass some sort of threshold that we can't fully quantify presently, (and we know that said threshold exists because it took the accumulation of three artifacts of Susano coming together for him to manifest without ANY deliberate summoning effort. He just MADE HIMSELF when enough targets of faith in him came together.) It's mentioned in many places, including the lore books, that the Far East has widespread belief in the way that Auspices come to exist, (explicitly, they believe in the process that Auspices go through as part of their local religious beliefs and mythology, along with belief in basically everything else ALSO having spirits.) which would absolutely qualify as collective Faith for the purposes of Primal manifestation.

So essentially, you do believe that their belief in Auspices and Tural Vidraal are akin to a belief in gravity; an observation of a thing that exists. That does raise a chicken-and-egg question in this setting that the Pilgrim's Traverse also put forward (what came first, the belief or the thing), but it's also not relevant for talking about the Elementals.

Because the Elementals are both an extant Thing, and an object of worship; Gridania's people both believe in them as a clearly evidenced phenomena, and as a higher power that they pray to. Because of this they can't be easily compared to the Auspices and Tural Vidraal, who only have one half of that. The Kami are a valid comparison, but one one without a lot of juice; there are maybe two storylines that focus on the Kami, and neither of them in a way that gives us workable information. No questions we have about the Elementals, and especially their relative strength as the OP was asking about, are answered by using comparisons to the Kami.