Hey, these are some solid turn-based RPG mechanics, here! I've never played Dicey Dungeons, so I can't speak to how it compares, but I will say that the name "Coiny Catacombs" as a riff on that is quite clever, haha.
I think the biggest thing that would improve your game would be some tweaks to the user interface. Once the player understands the pattern of what needs to be done, things move along in a predictable way, but some on-screen graphics and animation could help direct focus.
For example, in the middle of a fight, maybe have an arrow pointing at the coins and a hand icon to show you can click and drag them. The "flip again" button could be moved closer to where the coins are so it's more obvious they are related, and there could be an indicator that shows you can only re-flip once. While the coins are being dragged, the open slots could shine brighter. When it's the player's turn, maybe the enemy's skill info boxes can fade to a darker color so the focus is on the player's info. When the player can't do anything else during a turn, perhaps the "End Turn" button could be highlighted. Also, the information you have in the sliding side-panel could probably just be shown on screen between fights, so that it's easy to see HP changes based on the coin flips from different encounters.
Little things like that can help with the flow and teach players what they need to do even without written instructions. I know that might be a bit more polish than you had time for in a one week game jam, but just throwing out some suggestions.
Anyway, I think you managed to capture the classic RPG adventure feel pretty well given the time constraints. Nice job!