Hi there SGMMike,
To get started with your notification sound issue, we would recommend first making sure you have the latest iOS version, iOS 17.0.3, installed on your device: Update your iPhone or iPad - Apple Support. Once you've done that, the next step is to verify your Google app for the Nest is updated as well: How to manually update apps on your Apple device - Apple Support. Both these steps will set you up with all the latest available software and fixes for certain issues.
Should you still have an issue with the notification only for the Google Nest, try troubleshooting its app with the steps in If an app on your iPhone or iPad stops responding, closes unexpectedly, or won’t open - Apple Support.
For more help after that, please get in touch with Apple Support directly. They will have the tools and resources needed to further assist. You can do that here: Get Support
Have an amazing weekend.