I have to admit, I don't see the difference you seem to find so relevant.
And maybe part of the problem is due to your initial expectations and hopes about how to play the Priest (does God exists or not?) and your specifically "theist" way of intending religion.
Let's see if I can reframe the Priest for you :)
1) Player knowledge
When the player feels like having the Priest believe in god, that's a good day for the PC, their faith is strong and steady.
When the player feels like having the Priest not believe in god, that's a hard day for the PC, their faith is shaken and unsteady.
See? Free choice. Either way you can easily switch back and forth.
I mean, you could also play the Priest "upside down" :D
he PC might not believe in their deity. Maybe they never did, as they were indoctrinated but never truly bought in into the spiel. And then the player chooses to notice how a crop of flowers looks like a sign. And how the PC looks at a star constellation and feels an omen. Or how the words of a stranger resound full of meaning, although it probably is just a coincidence.
Maybe the Player starts the campaign choosing to apply their knowledge to the Priest, and later on develops the character is such a way that they will choose to NOT apply their knowledge, having the character "believe again" :D
And you said it yourself: the language of the moves is suggestive. Nothing else. You can then take what you want from it :)
The priest doesn't believe in their deity? Fine, but the ritual prayers STILL feature the deity's name, obviously. How does the Priest feel about that? Is it a bitter joke? Is it a comforting tradition? Is it puzzling and conflicting?
2) The core question
I don't know... maybe it's because I look at it from a different angle in general? Like... I don't care whether the deity exists or not. Not being able to EVER know makes the question uninteresting and irrelevant to me. Thus my focus shifts on to the religion itself: the preachings, the dogmas, the tenants, the values, the rituals, the traditions, etc...
The question is: do I believe that my religion is valid? are my inner feelings and beliefs aligned with my religion? are there pain points in my adherence to the religion? do I shape it, or does it shape me? and what about the rest of the world... how do they relate to my religion, and to me as one of its representatives?
THIS is the question at the core of the Priest.
I understand that it's a different question than what you initially expected. Sorry to disappoint ^_^
3) Ungodly Gods
One very interesting way in which I saw the Priest played a bunch of times is to simply sidestep the whole "guy in the sky" question at the diegetic level. Like... instead of a positive religion, why not play a philosophy?
Gods don't exist, but what if your religion is instead about "the universal balance"?
Game mechanics say that there is no "guy in the sky" but say nothing about... I don't know... Karma... or reality being a computer simulation... or kale being good for you... or being vegan.
There can be a religion based on ANY such things, and the Priest can believe them or not as they are, in game terms, an open question.
I had a campaign set is a sort of "mythological greece but in spaaace" where the Priest believed in "the golden triangle" ... a fundamental principle of geometric harmony. It was very believable, it played perfectly, it even sparked many scenes (often Bond scenes during a Long Rest move) where the Protagonists would discuss, debate, enquire about his religion :D
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So unless they only draw of the Priest was the "is god real or not?" question, then my suggestion would be to try, as a fun experiment, to play a Priest and see what happens :)
I personally would be very curious to know how the experience goes for you :D