Fix lobby: only show players who have joined

Changes:
- Added socket.join(LOBBY_ROOM) when player joins lobby
- Changed io.emit() to io.to(LOBBY_ROOM).emit() for all lobby events
- Players only see lobby events after they click JOIN LOBBY
- Fixed player list to update correctly when players join/ready
- Game now starts properly when all players are ready

Files modified:
- server/index.js: Use Socket.io rooms for lobby scoping
- public/js/app.js: Show lobby screen on player-joined event
- public/js/ui.js: Removed duplicate listener override

public/js/app.js

@@ -23,6 +23,10 @@ function setupNetworkListeners() {
   // Player joined lobby
   network.setListener('player-joined', (player) => {
     ui.updatePlayerList(network.getAllPlayers());
+    // Show lobby screen if we're on the login screen
+    if (ui.screens.room.classList.contains('active')) {
+      ui.showScreen('lobby');
+    }
   });
 
   // Player left lobby

public/js/ui.js

@@ -57,11 +57,6 @@ class UIManager {
       return;
     }
 
-    // Set listener for player joined event
-    network.setListener('player-joined', () => {
-      this.showScreen('lobby');
-    });
-
     network.joinLobby(playerName);
   }