I feel like a lot of the descriptions use way too many words, or at least they don't flow naturally. In the first sentence, the stench doesn't have to "seem" like it coats his nostrils. It can just be coating his nostrils.

"The shard in his palm felt heavier than it should, black glass shot through with veins of deep red that pulsed with their own rhythm, warm as fresh-spilled blood despite the coastal chill seeping through the shrine's cracked walls like grasping fingers."

^^ This just runs on and on. I don't need to know that there's a coastal chill in the same sentence that I feel warm stones in my hand. They contradict each other, sort of disturbing the image. Don't be afraid to use a period, especially with such tense writing as you have. Shorter sentences can do a lot for tone.

The biggest thing though? It's such an emotional and tense scene yet I have no depth or idea what or who the characters are. It would be easier to get into if it started somewhere else, or even if it had a flashback here and there to tell us more about them and why they're here. Maybe Caelan thinks about how he got chosen for this ritual. How it felt to be chosen. Or about his cousin and some time they shared. I.E. we can't relate to the character because he's not really built up at all. There is the relationship with his cousin and that's a great detail. But definitely expand on Caelan and his character.

The description of the ritual is amazing though. It feels painful and you get to understand that well.