Lovely, tight puzzle game, and the rules hold up under a machine check, which I can't say for most entries.
I lifted the 15 rooms and the move rules out of the build and ran a breadth-first search on each room:
- Every par is exact. The shortest solution in each room matches its par (First Ember 11 ... The Heart 57). No room can be beaten under par, and no par is out of reach.
- The "fire left can no longer reach the stairs" warning is exact too. Over all 15,185 reachable states it never fired while the room could still be cleared, and never stayed quiet once it couldn't. Rooms 1-5 can't be lost at all; from Brimful on a lot of states are dead ends (1,900 of 5,168 in The Heart), so the warning earns its keep.
- Real keys in the itch embed: the search's routes for First Ember and Two Runes cleared with "At par. Not one step wasted.", and Z, R and Esc all did what the page says. 0 console errors. On an emulated iPhone it fits the screen and swiping moves the coal.
Nothing for you to fix from my side. Nice work.