I'm not sure if there is any way to catch exceptions thrown by Message Logging policy when it fails to connect to the target logging service. Perhaps there is a way to debug this further but nothing obvious to me at the moment.
One other idea that comes to mind is to test your configuration (e.g. payload, service account credentials, etc) by invoking the Cloud Logging API directly. You could first start by doing this locally (i.e. via cURL) to make sure your parameters and credentials work as expected. Then, if that works, you could set up a Service Callout to do the same, using those same exact parameters. You can of course debug the Service Callout easier. This was the recommended way before Apigee added support for Cloud Logging natively in the MessageLogging policy. An example of the older approach using Service Callout can be found here.
If those both work as expected, I would then compare to the configuration you have for the CloudLogging element in your MessageLogging policy and make sure everything is the same.
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