I got the vibe their objective is to try and resurrect the witch, of which any magically inclined half elf may serve as a candidate. So, while catzilla may indeed be a raging Puck, I'd also entertain the possibility the cult succeeded and that's how he winds up if powered up by the witch.
Only problem I have with this whole process is it doesn't make sense for Subaru to have this resurrection ability if he's using it to stop the witch. All signs so far indicate it's a dark power, of which Betelguese seemingly picked up on and questioned if he was one of them. When Subaru first encountered the cult and they let him live, I'm also wondering if that was a masked Betelguese. What I'm thinking may be the case is his power is actually being bestowed by the dragon they've mentioned a few times throughout the show. The "stink of the witch" might be her attempting to strip him of it as it inevitably guarantees Subaru would succeed as long as he keeps trying and learning.
Then again, maybe Puck is actually a baby dragon.