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:

scripts/systems/room_navigator.gd

@@ -1,5 +1,5 @@
 ## RoomNavigator — autoload that moves the Camera2D smoothly between hospital floors.
-extends Node
+class_name RoomNavigator extends Node
 
 signal room_changed(floor_index: int)
 
@@ -19,11 +19,11 @@ func go_to_floor(floor_index: int) -> void:
 		return
 	_current_floor = floor_index
 	var target_y: float = floor_index * -FLOOR_HEIGHT
-	var tween: Tween = _camera.create_tween()
+	var tween: Tween = create_tween()
 	tween.set_ease(Tween.EASE_IN_OUT)
 	tween.set_trans(Tween.TRANS_SINE)
 	tween.tween_property(_camera, "position:y", target_y, CAMERA_TWEEN_DURATION)
-	room_changed.emit(floor_index)
+	tween.finished.connect(func() -> void: room_changed.emit(floor_index))
 
 
 func get_current_floor() -> int:

scripts/systems/settings_menu.gd

@@ -16,10 +16,12 @@ func hide_menu() -> void:
 
 func _on_music_slider_value_changed(value: float) -> void:
 	AudioManager.set_music_volume(value)
+	GameState.music_volume = value
 
 
 func _on_sfx_slider_value_changed(value: float) -> void:
 	AudioManager.set_sfx_volume(value)
+	GameState.sfx_volume = value
 
 
 func _on_reset_button_pressed() -> void: