fix(core): resolve review findings in Sprint 3-4

- Fix SaveManager reset_game to use DirAccess.remove correctly
- Add null check for FileAccess.open in save_game
- Fix AudioManager crossfade tween callback chain
- Replace fragile absolute HUD path with relative onready
- Guard character position save against empty id
- Add GameState.has_character_position helper
- Emit room_changed signal after tween completes
- Add target_floor validation in ElevatorButton
- Persist audio settings via GameState
- Add class_name to RoomNavigator, AudioManager, HUD

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

scripts/systems/hud.gd

@@ -1,11 +1,11 @@
 ## HUD — heads-up display with back button, music toggle, and settings access.
-extends CanvasLayer
+class_name HUD extends CanvasLayer
 
 const MUSIC_ON_SYMBOL: String = "♪"
 const MUSIC_OFF_SYMBOL: String = "✕"
 
 var _music_enabled: bool = true
-@onready var _settings_menu: SettingsMenu = get_node_or_null("/root/Main/UI/SettingsMenu") as SettingsMenu
+@onready var _settings_menu: SettingsMenu = get_node_or_null("../SettingsMenu") as SettingsMenu
 
 
 func _on_back_button_pressed() -> void: