Is there a public API I can poll for server/region degradations?

Edit: Directly to your question, The right place to get this information is via the AWS Health API which does require authentication in your account.

The type of event your are looking for is of the category "issue" which covers ongoing (or recent) service events.

You can use the command

aws health describe-events --filter eventTypeCategories=issue

https://docs.aws.amazon.com/health/latest/ug/supported-operations.html