Cosy Box Push Puzzle Game Builder

One prompt that builds a complete cosy box-pushing puzzle game in a single HTML file, art drawn in code, with two twists: every level is proven solvable by the game's own solver (best par moves and pushes shown), and solved levels bring a village back to life, piece by piece. 128 rooms in 4 chapters (ice, one-way gates, heavy crates), unlimited undo, deadlock warnings, hints from any position, a verifying level editor, daily room, quests, touch, synthesized music.