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/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: