fix: preserve gameStatus when switching game modes

- Stop passing gameMode as dependency to useGameStatus initialization
- Create useGameStatus once with default 'letters' mode
- Add setGameMode method to update mode via ref without recreating hook
- Update gameMode via effect in useGame when it changes
- Fixes issue where switching to letters mode and starting game would reset to waiting

src/types.ts

@@ -107,6 +107,7 @@ export type GameStatusManager = {
   updatePlayerX: (x: number) => void;
   handleTypedLetter: (letter: string) => void;
   setGameLoopCallback: (callback: (deltaTime: number, letters: FallingLetter[]) => void) => void;
+  setGameMode: (mode: GameMode) => void;
   addCorrect: () => void;
   addMissed: () => void;
   addDeath: () => void;