refactor: remove duplicate game control buttons from game phases

Remove duplicate New Game button from GamePhase and update ResultsPhase
to use proper arcade navigation now that controls are in the nav bar.

- Remove New Game button from GamePhase (now in nav)
- Change ResultsPhase "Back to Games" to "Back to Arcade"
- Add proper session exit in ResultsPhase arcade navigation

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

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

apps/web/src/app/arcade/matching/components/GamePhase.tsx

@@ -67,43 +67,6 @@ export function GamePhase() {
           )}
         </div>
 
-        {/* Game Controls */}
-        <div className={css({
-          display: 'flex',
-          alignItems: 'center',
-          gap: '12px'
-        })}>
-          {/* New Game Button */}
-          <button
-            className={css({
-              background: 'linear-gradient(135deg, #ffeaa7, #fab1a0)',
-              color: '#2d3436',
-              border: 'none',
-              borderRadius: '10px',
-              padding: { base: '8px 12px', sm: '10px 16px' },
-              fontSize: { base: '13px', sm: '14px' },
-              fontWeight: 'bold',
-              cursor: 'pointer',
-              transition: 'all 0.2s ease',
-              boxShadow: '0 2px 6px rgba(255, 234, 167, 0.3)',
-              _hover: {
-                transform: 'translateY(-1px)',
-                boxShadow: '0 3px 8px rgba(255, 234, 167, 0.5)',
-                background: 'linear-gradient(135deg, #fdcb6e, #e17055)'
-              }
-            })}
-            onClick={resetGame}
-          >
-            <div className={css({
-              display: 'flex',
-              alignItems: 'center',
-              gap: '6px'
-            })}>
-              <span>🔄</span>
-              <span>New Game</span>
-            </div>
-          </button>
-        </div>
       </div>
 
       {/* Player Status Bar */}

apps/web/src/app/arcade/matching/components/ResultsPhase.tsx

@@ -270,11 +270,12 @@ export function ResultsPhase() {
             }
           })}
           onClick={() => {
-            console.log('🔄 ResultsPhase: Navigating to games with Next.js router (no page reload)')
-            router.push('/games')
+            console.log('🔄 ResultsPhase: Exiting session and navigating to arcade')
+            exitSession()
+            router.push('/arcade')
           }}
         >
-          🏠 Back to Games
+          🏟️ Back to Arcade
         </button>
       </div>
     </div>