Reset lobby UI state when returning from game over

- Add resetLobbyState() to UIManager to clear player lists and reset ready button
- Call resetLobbyState() when player-joined event has null player (game over reset)
- Reset ready button state in endGame() before showing game over screen

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

public/js/ui.js

@@ -80,9 +80,24 @@ class UIManager {
 
   handleBackToLobby() {
     this.hideGameOver();
+    this.resetLobbyState();
     this.showScreen('room');
   }
 
+  resetLobbyState() {
+    // Reset ready button to default state
+    this.buttons.ready.textContent = 'READY';
+    this.buttons.ready.disabled = true;
+
+    // Clear player and spectator lists
+    this.displays.playerList.innerHTML = '';
+    this.displays.spectatorList.innerHTML = '';
+
+    // Reset game room name
+    this.displays.gameRoomName.textContent = 'GLOBAL LOBBY';
+    this.displays.gameRoomName.classList.remove('spectator-mode');
+  }
+
   updatePlayerList(players) {
     this.displays.playerList.innerHTML = '';
     Object.values(players).forEach(player => {