The app is no longer stuck restarting and the 503 has been resolved. A transient network issue was also occurring that coincided with Emergency Network Maintenance done by our hosting provider.
A mitigation has been put in place which has resolved the issue. A longer term fix will be worked on to fully resolve the issue. The cause was a recent adoption of a sign-in feature that Google rolled out seemingly unannounced, which broke our system's sign-in flow. The mitigation adds support for this feature at a higher-level which removes the need for the app code to change. The long term fix will be to update the application so it supports this new feature.