feat: Implement comprehensive lobby system with main menu, room management, and loading screen.

scripts/managers/lobby_manager.gd

@@ -290,19 +290,21 @@ func leave_room() -> void:
 	reset()
 	_stop_lan_broadcast()
 	
+	# Emit before nulling peer so UI can still access peer info if needed
+	emit_signal("room_left")
+	
 	if is_lan_mode:
-		# LAN mode: just close the ENet peer directly
-		if multiplayer.has_multiplayer_peer():
-			multiplayer.set_multiplayer_peer(null)
-		is_lan_mode = false
+		# LAN mode: Host should keep peer alive long enough to reach lobby
+		if not is_host or get_tree().current_scene.name == "Lobby":
+			if multiplayer.has_multiplayer_peer():
+				multiplayer.set_multiplayer_peer(null)
+			is_lan_mode = false
 	else:
 		# Nakama mode: full Nakama cleanup
 		NakamaManager.cleanup()
 		
 	# Important: Clean up game state as well to prevent ghost players
 	GameStateManager.reset()
-	
-	emit_signal("room_left")
 
 func refresh_room_list() -> void:
 	"""Request updated room list from Nakama or scan for LAN rooms."""