chore: improve logging in arcade session management

Added detailed logging to help debug player ID vs user ID flow:
- useArcadeSocket: Log full move payload with JSON stringification
- session-manager: Log player ID, game state players, and phase info

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

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

apps/web/src/hooks/useArcadeSocket.ts

@@ -124,8 +124,9 @@ export function useArcadeSocket(events: ArcadeSocketEvents = {}): UseArcadeSocke
       console.warn('[ArcadeSocket] Cannot send move - socket not connected')
       return
     }
-    console.log('[ArcadeSocket] Sending move:', move)
-    socket.emit('game-move', { userId, move })
+    const payload = { userId, move }
+    console.log('[ArcadeSocket] Sending game-move event with payload:', JSON.stringify(payload, null, 2))
+    socket.emit('game-move', payload)
   }, [socket])
 
   const exitSession = useCallback((userId: string) => {

apps/web/src/lib/arcade/session-manager.ts

@@ -129,9 +129,22 @@ export async function applyGameMove(
   // Get the validator for this game
   const validator = getValidator(session.currentGame as GameName)
 
+  console.log('[SessionManager] About to validate move:', {
+    moveType: move.type,
+    playerId: move.playerId,
+    gameStateCurrentPlayer: (session.gameState as any)?.currentPlayer,
+    gameStateActivePlayers: (session.gameState as any)?.activePlayers,
+    gameStatePhase: (session.gameState as any)?.gamePhase
+  })
+
   // Validate the move
   const validationResult = validator.validateMove(session.gameState, move)
 
+  console.log('[SessionManager] Validation result:', {
+    valid: validationResult.valid,
+    error: validationResult.error
+  })
+
   if (!validationResult.valid) {
     return {
       success: false,