EPIC: Gameplay State, Persistence, and Motion Execution

[jasonappah]

Goal: Make loading/resuming games deterministic and safe while improving motion execution quality. Scope includes: 1) restore robot pose when loading saves; 2) gate command dispatch so robots only move when a game is actually running/resuming; 3) align command queueing/execution with game phases; 4) add path math unit tests; 5) add per-move execution timeouts with safe cancellation and surfaced errors. Key code: src/server/api/save-manager.ts, src/server/api/game-manager.ts, src/server/command/*, src/server/robot/position.ts, src/server/robot/path-materializer.ts, src/server/robot/grid-indices.ts, src/common/spline.ts, src/server/api/socket-manager.ts. Acceptance: Loading a saved game reconstructs board+robot state; commands only dispatch in the Running phase; moves timeout safely; tests cover typical and edge paths.