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/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: