fix: set room sessions to use /arcade/room URL

When creating an arcade session for a room-based game, the gameUrl was
hardcoded to '/arcade/matching'. This caused useArcadeRedirect to
redirect users from /arcade/room to /arcade/matching, breaking the
simplified room addressing model.

Fix:
- Changed gameUrl to '/arcade/room' for room-based sessions
- Now users stay on /arcade/room for the duration of room gameplay
- Solo sessions still use game-specific URLs like /arcade/matching

This ensures the user experience matches the intended design:
- /arcade/room - room-based multiplayer (regardless of game type)
- /arcade/[game] - solo/local multiplayer for specific games

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

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

apps/web/socket-server.ts

@@ -142,7 +142,7 @@ export function initializeSocketServer(httpServer: HTTPServer) {
             await createArcadeSession({
               userId: data.userId,
               gameName: 'matching',
-              gameUrl: '/arcade/matching',
+              gameUrl: '/arcade/room', // Room-based sessions use /arcade/room
               initialState,
               activePlayers,
               roomId: room.id,