Implement Katamino, a 5×N grid tiling puzzle using the 12 standard
pentominoes. Players select a grid width (3-12) and solve puzzles by
placing all chosen pieces to fill the board.
Key features:
- Three-screen flow: penta select → set select → play
- Scrollable puzzle card grid with completion progress tracking
- Piece rotation (R), flip (F), and lift-to-reposition
- Pre-generated puzzle bank (katamino.json) with all valid tilings
- Offline generator script (genKatamino.js) using backtracking solver
- Progress saved to localStorage per puzzle
- Registration in server registry and scene dispatchers
