The issue was that my app was being suspended by iOS in the background before it could prepare and play the sound. To fix this, I used a background task to request execution time from the system while preparing and playing the audio.

var bgTask: UIBackgroundTaskIdentifier = .invalid

func beginBackgroundTask() {
    bgTask = UIApplication.shared.beginBackgroundTask {
        UIApplication.shared.endBackgroundTask(self.bgTask)
        self.bgTask = .invalid
    }
}

Call beginBackgroundTask right before your code to play the audio.

beginBackgroundTask()
guard let url = Bundle.main.url(forResource: "TimerDone", withExtension: "wav") else { return }
do {
    audioPlayer = try AVAudioPlayer(contentsOf: url)
    audioPlayer?.play()
} catch {
    print("Audio playback error: \(error.localizedDescription)")
}