fix(card-sorting): New Game now restarts with same settings instantly

Changed "New Game" behavior to immediately start a new game with the
current settings, without going through the setup page.

Changes:
- Removed the gamePhase === 'playing' guard in startGame()
- This allows starting a new game even when already playing
- Still prevents rapid double-sends within 500ms
- Simplified GameComponent's onNewGame handler back to just calling startGame()

Now when "New Game" is clicked:
- Immediately starts a fresh game
- Uses the same settings (card count, show numbers, time limit, game mode)
- No interruption with the setup screen

This provides a smoother "play again" experience for quick restarts.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

apps/web/src/arcade-games/card-sorting/Provider.tsx

@@ -404,13 +404,11 @@ export function CardSortingProvider({ children }: { children: ReactNode }) {
       return
     }
 
-    // Prevent multiple simultaneous START_GAME moves when multiple clients
+    // Prevent rapid double-sends within 500ms to avoid duplicate game starts
-    // click "Play Again" at the same time. Only allow if we're NOT already starting/in a game.
-    // Also check if we just started a game (within 500ms) to prevent rapid double-sends.
     const now = Date.now()
     const justStarted = state.gameStartTime && now - state.gameStartTime < 500
 
-    if (state.gamePhase === 'playing' || justStarted) {
+    if (justStarted) {
       return
     }
 

apps/web/src/arcade-games/card-sorting/components/GameComponent.tsx

@@ -41,16 +41,7 @@ export function GameComponent() {
           : undefined
       }
       onNewGame={() => {
-        // If currently playing, go to setup first to clean up, then start immediately
+        startGame()
-        if (state.gamePhase === 'playing') {
-          goToSetup()
-          // Use a small delay to let setup phase render, then start new game
-          setTimeout(() => {
-            startGame()
-          }, 100)
-        } else {
-          startGame()
-        }
       }}
     >
       <StandardGameLayout>