Add Takuzu+ and polish menu/game interactions

[FelineStateMachine]

Summary

• add Takuzu+ as a new puzzle type, including generation logic, saves/imports, mouse support, help/docs, tests, and PDF/JSONL export with relation-clue instructions
• rework the play flow with a filterable category picker, category detail pane, specific-game seeded puzzle selection, and Escape-based return-to-menu behavior
• polish dynamic grid rendering and in-game UX across several puzzles, including mouse hit-testing, crosshair/bridge highlighting, status/help copy updates, and related test coverage

Testing

• go test ./...